EC3115 - Chapter 12 Quiz: Monetary Policy Uncertainties

1. According to the analysis of data revisions, which of the following is NOT a property of a 'well-behaved' data revision?

The revision should have a mean of zero. The revision should be predictable using information available at the time of the initial announcement. The variance of the final revision should be small compared to the variance of the final data value. The initial announcement should be an unbiased estimate of the final value.

Correct Answer: B.

A 'well-behaved' data revision is considered 'news' rather than 'noise'. If a revision is 'news', it represents the arrival of new, unforeseeable information. Therefore, it should NOT be predictable based on the information set available when the initial forecast or announcement was made. If a revision is predictable, it implies that the initial announcement was not an optimal or rational forecast, violating a key assumption of modern macroeconomics.

Source: EC3115 Subject Guide, Chapter 12; Aruoba (2008), 'Data revisions are not well-behaved'.

2. In Poole's (1970) model, if an economy is primarily subject to shocks originating from the goods market (unstable IS curve), which monetary policy instrument is optimal for minimizing output fluctuations?

Targeting the money supply. Targeting the interest rate. Targeting the exchange rate. A combination of money supply and interest rate targets.

Correct Answer: A.

When IS shocks dominate, targeting the money supply is superior. A fixed money supply (a fixed LM curve) allows the interest rate to act as an automatic stabilizer. For example, a positive IS shock (a rightward shift) would push output and interest rates up. The higher interest rate crowds out some investment, partially offsetting the initial shock and dampening the output fluctuation. Conversely, fixing the interest rate would require the central bank to increase the money supply to prevent the interest rate from rising, thereby fully accommodating the IS shock and maximizing the resulting output volatility.

Source: Poole (1970), 'Optimal choice of monetary policy instrument...'; EC3115 Lecture Slides, Unit L.

3. What is the core implication of Brainard's (1967) analysis of parameter uncertainty for the conduct of monetary policy?

Policy should be aggressive to overcome the uncertainty. The central bank should ignore parameter uncertainty as it averages out over time. Policy should be more cautious or gradual than it would be under certainty. The central bank should switch to fiscal policy as its primary tool.

Correct Answer: C.

Brainard's key finding is that uncertainty about the magnitude of policy effects (parameter or multiplicative uncertainty) leads to policy attenuation or conservatism. Because the policymaker's actions affect the variance of the outcome, a large policy move risks a large error if the true parameter value is different from the estimate. A risk-averse policymaker will therefore trade off some of the expected gain from closing an output or inflation gap for a reduction in the variance of the outcome. This leads to a more cautious, gradualist approach, often referred to as 'Brainard conservatism'.

Source: Brainard (1967), 'Uncertainty and effectiveness of policy'; EC3115 Subject Guide, Chapter 12.

4. The principle of 'certainty equivalence' suggests that policymakers should respond to the expected values of variables as if they were certain. This principle breaks down in the presence of:

Additive uncertainty only. Both additive and parameter uncertainty. Any type of shock to the economy. Parameter (multiplicative) uncertainty.

Correct Answer: D.

Certainty equivalence holds when the uncertainty is purely additive (e.g., random shocks to the IS or LM curve that are independent of the policy instrument). In this case, the policy instrument only shifts the mean of the target variable's distribution, not its variance. The optimal policy is to act on expected values. However, when there is parameter (multiplicative) uncertainty, the policy instrument itself affects the variance of the target variable. The policymaker must then consider this impact on variance, and certainty equivalence no longer applies. The optimal policy will differ from one based solely on expected values.

Source: EC3115 Subject Guide, Chapter 12; Brainard (1967).

5. Aruoba (2008) finds that for many US macroeconomic variables, data revisions are not 'well-behaved'. What does the finding that revisions have a non-zero mean imply?

Initial announcements are biased estimates of the final data. The data revisions are pure 'news'. The economy is more volatile than initially reported. The statistical agencies are behaving irrationally.

Correct Answer: A.

If data revisions were 'well-behaved', they would have a mean of zero, meaning that over time, the upward and downward revisions cancel out. A persistent non-zero mean (e.g., consistently positive) implies that the initial announcements are systematically under- or over-estimating the final, true value. This means the initial announcements are biased estimates.

Source: Aruoba (2008), 'Data revisions are not well-behaved'; EC3115 Subject Guide, Chapter 12.

6. In Poole's (1970) model, if the money market is highly unstable (e.g., due to financial innovation causing volatile money demand), which policy instrument is preferred?

Money supply targeting. Interest rate targeting. A fixed exchange rate peg. No policy intervention.

Correct Answer: B.

When the LM curve is unstable due to shocks in the money market (volatile money demand), targeting the interest rate is the optimal strategy. By fixing the interest rate, the central bank effectively insulates the real economy (the IS curve) from these financial shocks. The central bank achieves this by adjusting the money supply to meet whatever the demand is at the target interest rate, thus preventing the LM curve from shifting and affecting output. In this scenario, money supply targeting would transmit the financial volatility directly to the interest rate and, consequently, to output.

Source: Poole (1970); EC3115 Lecture Slides, Unit L.

7. If a data revision is classified as 'noise', what does this imply about the initial data announcement?

It was an efficient forecast of the final value. The revision is uncorrelated with the final value. The initial announcement is an observation of the final series measured with error. The revision is unpredictable.

Correct Answer: C.

The 'noise' hypothesis, as described by Mankiw, Runkle, and Shapiro (1984) and discussed in Aruoba (2008), posits that the initial data release is the 'true' final value plus some measurement error (the noise). This means the revision (which removes the error) will be correlated with the initial announcement but uncorrelated with the true final value. This contrasts with the 'news' view, where the initial release is an efficient forecast and the revision is the forecast error.

Source: Aruoba (2008); EC3115 Subject Guide, Chapter 12.

8. Under parameter uncertainty, the optimal policy choice involves a trade-off between:

Closing the expected output gap and reducing output volatility. Inflation and unemployment. Current consumption and future consumption. Fiscal dominance and monetary dominance.

Correct Answer: A.

With parameter uncertainty, an aggressive policy to fully close the expected output gap also significantly increases the variance (volatility) of output. A risk-averse central bank will therefore not pursue this aggressive policy. Instead, it chooses a more cautious stance, accepting that the expected output gap will not be fully closed in exchange for a lower and more acceptable level of output volatility. This is the fundamental policy trade-off introduced by parameter uncertainty.

Source: Brainard (1967); EC3115 Lecture Slides, Unit L.

9. In the Brainard model, if the policy multiplier `g` in the equation `y = gX` has a mean `ĝ` and a variance `σ_g^2`, the optimal policy `X` is given by `X = (ĝy*) / (ĝ^2 + σ_g^2)`. What happens to the optimal policy `X` as uncertainty `σ_g^2` increases?

`X` increases, indicating a more aggressive policy. `X` remains unchanged due to certainty equivalence. `X` becomes negative. `X` decreases, indicating a more cautious policy.

Correct Answer: D.

The formula for the optimal policy is \( X = \frac{\hat{g}y^*}{\hat{g}^2 + \sigma_g^2} \). As the variance of the multiplier, \( \sigma_g^2 \), increases, the denominator of the fraction becomes larger. This causes the overall value of `X` to decrease. A smaller `X` represents a less aggressive use of the policy instrument. This mathematically demonstrates the principle of policy attenuation: greater uncertainty leads to greater caution.

Source: EC3115 Subject Guide, Chapter 12.

10. Additive uncertainty, such as random shocks to aggregate demand, is distinct from parameter uncertainty because:

It always leads to policy conservatism. It does not violate the certainty equivalence principle. It is a result of measurement error in policy instruments. It can be eliminated by better forecasting.

Correct Answer: B.

The key distinction is its effect on the variance of the policy outcome. With purely additive uncertainty (that is independent of the policy instrument), the policymaker's actions do not change the variance of the outcome; they only shift its mean. Therefore, the optimal strategy is to act on the expected values as if they were certain, which is the definition of certainty equivalence. Parameter uncertainty, in contrast, makes the outcome's variance dependent on the policy action, thus breaking certainty equivalence.

Source: EC3115 Subject Guide, Chapter 12; Brainard (1967).

11. The historical shift by many central banks (like the US Fed) from money supply targeting in the 1970s to interest rate targeting in the 1980s can be best explained by:

A period of highly unstable government spending (IS shocks). The rise of monetarism as a dominant economic theory. A wave of financial innovation that led to instability in money demand (LM shocks). A political decision to simplify the communication of monetary policy.

Correct Answer: C.

According to the Poole analysis, the choice of instrument depends on the dominant source of economic shocks. The 1980s were marked by significant financial innovation (e.g., new financial products, deregulation) which made the relationship between money supply, income, and interest rates unstable. This manifested as dominant LM shocks. In such an environment, interest rate targeting is the superior strategy to insulate the real economy from this financial volatility.

Source: EC3115 Lecture Slides, Unit L.

12. If a central bank follows the certainty equivalence principle, how does it conduct policy?

It sets its policy instruments based on the expected values of target variables, ignoring the variance of those variables. It always acts cautiously, setting its instruments to only partially close any expected gaps. It waits for final, revised data before making any policy decisions. It uses a combination of all available instruments to diversify risk.

Correct Answer: A.

Certainty equivalence means to 'act on the basis of expected values as if they were certain'. The policymaker calculates the expected path of the economy and sets the policy instrument to the level that would be optimal if these expectations were to be realized with certainty. This approach is only optimal under specific conditions, namely when uncertainty is purely additive and not affected by the policy instrument.

Source: EC3115 Subject Guide, Chapter 12.

13. In the context of data revisions, if the revision is considered 'news', then the revision should be:

Correlated with the initial announcement. Correlated with past data revisions. Small in magnitude. Uncorrelated with information available at the time of the initial announcement.

Correct Answer: D.

The 'news' hypothesis states that the initial announcement is an efficient, rational forecast based on all available information. The subsequent revision is the forecast error, which reflects new information that was not available at the time of the forecast. By definition, a rational forecast error must be uncorrelated with any information that was available when the forecast was made. If it were correlated, that information could have been used to improve the initial forecast.

Source: Aruoba (2008); EC3115 Subject Guide, Chapter 12.

14. Under parameter uncertainty, why does a central bank not want to set its policy instrument to fully close the expected output gap?

Because it is impossible to measure the output gap accurately. Because doing so would unacceptably increase the variance (volatility) of the output. Because the expected output gap is always zero on average. Because of political pressure to maintain a stable policy stance.

Correct Answer: B.

The essence of Brainard's analysis is the trade-off between the mean and variance of the policy target. A more aggressive policy that aims to fully close the expected gap (the mean) also multiplies the uncertainty about the policy's effect, leading to a higher variance of the outcome. A risk-averse policymaker finds this high variance undesirable and will therefore choose a less aggressive policy, accepting a persistent expected gap in return for lower volatility.

Source: Brainard (1967); EC3115 Lecture Slides, Unit L.

15. In the Poole model, what is the effect of an interest rate target when the economy experiences a positive shock to money demand (a rightward shift of the LM curve)?

Output remains stable at the target level. Output increases significantly. Output decreases significantly. The interest rate rises, partially offsetting the shock.

Correct Answer: A.

A positive shock to money demand would, ceteris paribus, increase the interest rate for any given level of income and money supply. If the central bank is targeting the interest rate, it will intervene to prevent this rise. It does so by increasing the money supply to fully accommodate the shock. The LM curve effectively does not shift from the perspective of the IS curve, and the equilibrium point of output and the (targeted) interest rate remains unchanged. The policy perfectly insulates output from the financial shock.

Source: Poole (1970); EC3115 Lecture Slides, Unit L.

16. Brainard's (1967) analysis shows that when pursuing a single target with multiple policy instruments under parameter uncertainty, it is generally optimal to:

Use only the most powerful instrument. Use only the instrument with the least uncertainty. Use a combination of all available instruments. Alternate between instruments in different periods.

Correct Answer: C.

This is a key result from Brainard's paper, analogous to portfolio diversification in finance. Each instrument has an uncertain impact. By using a combination of instruments, the policymaker can create a 'policy portfolio' whose overall impact is less uncertain than the impact of any single instrument used alone (unless their impacts are perfectly correlated). This diversification allows the policymaker to achieve a better trade-off between closing the target gap and controlling the variance of the outcome.

Source: Brainard (1967), 'Uncertainty and effectiveness of policy'.

17. The equation for output variance under a money supply target in Poole's model is \( Var(Y|M) = (\frac{1}{d+be})^2 (d^2\sigma_\epsilon^2 + b^2\sigma_\eta^2) \). If there are no money market shocks (\(\sigma_\eta^2 = 0\)), this simplifies to:

0 \( (\frac{d}{d+be})^2 \sigma_\epsilon^2 \) \( \sigma_\epsilon^2 \) \( (\frac{b}{d+be})^2 \sigma_\eta^2 \)

Correct Answer: B.

If \( \sigma_\eta^2 = 0 \), the term \(b^2\sigma_\eta^2\) in the original equation becomes zero. The equation for the variance of output then simplifies to \( Var(Y|M) = (\frac{1}{d+be})^2 (d^2\sigma_\epsilon^2) \), which can be rewritten as \( (\frac{d}{d+be})^2 \sigma_\epsilon^2 \). This is less than the variance under an interest rate target (which is \( \sigma_\epsilon^2 \)), confirming that money supply targeting is superior when only IS shocks are present.

Source: EC3115 Subject Guide, Chapter 12; Poole (1970).

18. Which statement accurately describes the graphical representation of the policy trade-off under parameter uncertainty (in mean-standard deviation space)?

The policy constraint is a vertical line. The indifference curves are straight lines. The optimal policy is where the policy constraint intersects the vertical axis. The optimal policy is at the tangency point between an indifference curve and a linear policy constraint, resulting in an expected output below the target level.

Correct Answer: D.

The policy constraint shows the feasible combinations of mean output (\(\hat{y}\)) and standard deviation of output (\(\sigma_y\)) that the policymaker can achieve. It is a straight line starting from the origin (in deviation form). The indifference curves are circular, centered on the target output level (on the vertical axis). The optimal point is the tangency between the policy constraint and the highest attainable indifference curve. Because the indifference curves are downward sloping below the target, this tangency point will always be at an expected output level below the target, illustrating the cautious policy stance.

Source: EC3115 Lecture Slides, Unit L; EC3115 Subject Guide, Chapter 12.

19. Additive uncertainty is so-named because:

The shock term is added to the equation for the target variable (e.g., \(Y = a - bR + \epsilon\)). It requires adding more policy instruments to be effective. The uncertainty adds up over time, becoming larger. It is the sum of data uncertainty and parameter uncertainty.

Correct Answer: A.

The term 'additive' refers to the mathematical structure of the model. The uncertainty enters as a separate, additive term in the equation. For example, in the IS curve \(Y = a - bR + \epsilon\), the shock \(\epsilon\) is added to the deterministic part of the equation. This is in contrast to multiplicative (parameter) uncertainty, where the uncertainty enters by multiplying a policy variable, as in \(Y = gX\) where `g` is random.

Source: EC3115 Subject Guide, Chapter 12.

20. According to Aruoba (2008), the empirical finding that data revisions are predictable is evidence against which hypothesis?

The 'noise' hypothesis. The efficient markets hypothesis. The 'news' hypothesis. The rational expectations hypothesis.

Correct Answer: C.

The 'news' hypothesis posits that initial announcements are rational forecasts and revisions are the result of new, unpredictable information. A key testable implication is that these revisions should be unpredictable based on information available at the time of the initial announcement. Aruoba's finding that revisions *are* predictable (i.e., they are correlated with the initial announcement and other known variables) is direct evidence against the 'news' hypothesis. It suggests the initial announcements were not fully rational forecasts.

Source: Aruoba (2008), 'Data revisions are not well-behaved'.

21. In the Brainard model, the degree of policy attenuation depends on the coefficient of variation of the policy multiplier, \(V = \sigma_a / \bar{a}\). A larger coefficient of variation leads to:

A more aggressive policy response. A more cautious policy response (greater attenuation). No change in the policy response. A switch to a different policy instrument.

Correct Answer: B.

The coefficient of variation measures the uncertainty of the multiplier relative to its mean effect. A larger value means the multiplier is less predictable. The optimal policy is to fill a fraction \(1 / (1 + V^2)\) of the gap. As \(V\) increases, \(V^2\) increases, the denominator \(1 + V^2\) increases, and the fraction of the gap to be filled decreases. This implies a more cautious, or attenuated, policy response.

Source: Brainard (1967); EC3115 Lecture Slides, Unit L.

22. Which of the following scenarios best describes a situation of pure additive uncertainty where certainty equivalence would hold?

The central bank is unsure how much a 1% change in interest rates will affect inflation. The effect of interest rates on inflation changes unpredictably over time. The central bank knows the inflation model perfectly, but private sector expectations are random. The central bank knows the inflation model perfectly, but there are unpredictable, random cost-push shocks to inflation.

Correct Answer: D.

Certainty equivalence holds when the model parameters are known, but there is an additive shock term that is random but whose properties (e.g., zero mean) are known. Option D describes this exactly: the model is known ('knows the inflation model perfectly'), but there is an additive shock ('random cost-push shocks'). Options A and B describe parameter uncertainty, where the multiplier effect of the policy instrument is unknown, which is precisely the condition that breaks certainty equivalence.

Source: EC3115 Subject Guide, Chapter 12.

23. In the Poole model, if the IS curve is perfectly stable (\(\sigma_\epsilon^2 = 0\)) but the LM curve is subject to shocks, the variance of output under an interest rate target is:

Zero. Equal to the variance of the LM shocks. Infinite. Smaller than the variance under a money supply target, but positive.

Correct Answer: A.

If the IS curve is stable, all shocks originate from the money market (the LM curve). By setting an interest rate target, the central bank completely insulates the goods market from these shocks. Any shock that would shift the LM curve is immediately offset by a change in the money supply to keep the interest rate fixed. As a result, the equilibrium level of output does not change, and its variance is zero. This is the scenario where interest rate targeting is perfectly effective.

Source: Poole (1970); EC3115 Subject Guide, Table 12.1.

24. The concept of 'interest rate smoothing' as a practical policy approach can be seen as a response to:

A legal requirement for central banks to avoid volatility. The desire to make monetary policy decisions less frequently. The presence of parameter uncertainty, as suggested by Brainard's work. The dominance of IS shocks in the economy.

Correct Answer: C.

Interest rate smoothing, the practice of adjusting policy rates in small, sequential steps, is a practical manifestation of Brainard conservatism. Faced with uncertainty about the structure of the economy and the effects of their policies (parameter uncertainty), central bankers act cautiously. Small, gradual moves allow them to learn more about the state of the economy and the effects of their actions before committing to a large, potentially destabilizing policy change.

Source: EC3115 Subject Guide, Chapter 12.

25. If a central bank observes that its initial estimates of GDP growth are consistently revised upwards three months later, this suggests that:

The data revisions are pure 'news'. The initial GDP announcements are biased downwards and the revisions contain 'noise'. The economy is fundamentally unpredictable. The final GDP data is unreliable.

Correct Answer: B.

A consistent upward revision means the revisions have a positive mean. This directly implies that the initial announcements are biased downwards. Furthermore, the fact that this is a predictable pattern ('consistently revised upwards') means the revisions are not pure 'news'. They contain a predictable component, which is characteristic of 'noise' or a failure of the initial announcement to be a rational forecast.

Source: Aruoba (2008); EC3115 Subject Guide, Chapter 12.

26. In the Poole model, the choice between an interest rate and a money supply instrument depends on:

The slope of the Phillips Curve. The level of government debt. The central bank's inflation target. The relative variances of shocks to the IS and LM curves.

Correct Answer: D.

This is the central conclusion of Poole's (1970) paper. The policymaker's goal is to minimize output variance. The analysis shows that the output variance resulting from each policy choice is a function of the variances of the shocks to the goods market (IS curve, \(\sigma_\epsilon^2\)) and the money market (LM curve, \(\sigma_\eta^2\)). The optimal instrument is the one that produces the lower output variance, which depends entirely on the relative sizes of these two shock variances.

Source: Poole (1970).

27. Which type of uncertainty is the primary focus of Poole's (1970) model?

Additive uncertainty. Parameter uncertainty. Model uncertainty. Knightian uncertainty.

Correct Answer: A.

Poole's model assumes that the parameters of the IS and LM curves (the multipliers and sensitivities) are known with certainty. The uncertainty enters through random, additive shock terms (\(\epsilon\) for the IS curve and \(\eta\) for the LM curve). This is a classic case of additive uncertainty, which allows for the analysis of instrument choice without the complications of parameter uncertainty introduced by Brainard.

Source: Poole (1970); EC3115 Subject Guide, Chapter 12.

28. Which type of uncertainty is the primary focus of Brainard's (1967) model?

Additive uncertainty. Data revision uncertainty. Parameter uncertainty. Uncertainty about the central bank's objective function.

Correct Answer: C.

Brainard's seminal contribution was to analyze the implications of uncertainty about the effectiveness of policy. In his model, \(y = gX\), the uncertainty is about the true value of the policy multiplier, `g`. This is known as parameter uncertainty or multiplicative uncertainty, as the random parameter multiplies the policy instrument. This is distinct from additive shocks, which are the focus of Poole's work.

Source: Brainard (1967); EC3115 Subject Guide, Chapter 12.

29. In the Brainard model, if a central bank follows Brainard's principle of conservatism, its policy actions will likely result in:

The output gap being closed faster than under certainty. The expected level of output remaining below its target level. Increased volatility in both inflation and output. The certainty equivalence principle being upheld.

Correct Answer: B.

Policy conservatism or attenuation means that the central bank deliberately does not apply the full dose of policy required to close the expected output gap. It 'undershoots' the target for the mean to reduce the variance of the outcome. As a result, the equilibrium under this optimal but cautious policy will be one where the expected level of output is below the ultimate target \(y^*\).

Source: Brainard (1967); EC3115 Lecture Slides, Unit L.

30. In the Poole model, what is the effect of a money supply target when the economy experiences a positive shock to investment spending (a rightward shift of the IS curve)?

Output is completely stabilized. The money supply increases to accommodate the shock. The interest rate falls, amplifying the shock. The interest rate rises, partially offsetting the increase in output.

Correct Answer: D.

With a money supply target, the LM curve is fixed. A positive IS shock (a rightward shift) will move the equilibrium point up along the fixed LM curve. This results in both higher output and a higher interest rate. The rise in the interest rate serves as an automatic stabilizer, as it 'crowds out' some of the interest-sensitive spending, thereby dampening the initial expansionary impact of the shock. This is why money supply targeting is preferred when IS shocks are dominant.

Source: Poole (1970); EC3115 Lecture Slides, Unit L.

31. The New Keynesian model with additive shocks presented in the Subject Guide (\(\pi_t = a\pi_{t-1} - bi_t + \epsilon_t\)) leads to a policy rule \(i_t = (a\pi_{t-1} - \pi^*)/b\). This outcome, where the optimal policy is unaffected by the presence of the shock term \(\epsilon_t\), is an example of:

The certainty equivalence principle. Brainard conservatism. The Taylor principle. Time inconsistency.

Correct Answer: A.

The optimal policy rule is derived by minimizing the expected loss function. Because the shock \(\epsilon_t\) is additive and its expected value is zero, it drops out of the first-order condition. The resulting policy rule is identical to the rule that would be derived if there were no shocks at all (i.e., if \(\epsilon_t = 0\) with certainty). This is a direct illustration of the certainty equivalence principle.

Source: EC3115 Subject Guide, Chapter 12.

32. Now consider the New Keynesian model where the parameter `b` is uncertain: \(\pi_t = a\pi_{t-1} - b_t i_t + \epsilon_t\), with \(b_t \sim (\bar{b}, \sigma_b^2)\). The optimal policy rule becomes \(i_t = (a\pi_{t-1} - \pi^*)\bar{b} / (\sigma_b^2 + \bar{b}^2)\). This demonstrates:

That policy should be more aggressive to counter the uncertainty in `b`. That certainty equivalence still holds because the shock \(\epsilon_t\) is still additive. That policy should be attenuated (less aggressive) due to parameter uncertainty. That the central bank should target the money supply instead.

Correct Answer: C.

This is a direct application of Brainard's result. The term \(\sigma_b^2\) in the denominator means that the policy response \(i_t\) is smaller in magnitude than it would be if `b` were known with certainty (where \(\sigma_b^2 = 0\)). The presence of parameter uncertainty (the randomness of \(b_t\)) causes the central bank to set its instrument less aggressively. This is policy attenuation or conservatism.

Source: EC3115 Subject Guide, Chapter 12.

33. Which of the following is an example of parameter uncertainty for a central bank?

Not knowing the latest quarterly GDP growth figure. An unexpected rise in oil prices. A sudden crash in the stock market. Not knowing the precise value of the marginal propensity to consume.

Correct Answer: D.

Parameter uncertainty refers to uncertainty about the structural coefficients of the economic model. The marginal propensity to consume is a key parameter in the IS curve that determines the size of the fiscal and monetary policy multipliers. Not knowing its precise value means the central bank is uncertain about the magnitude of the effect its policy actions will have on the economy. The other options are examples of data uncertainty (A) or additive shocks (B, C).

Source: EC3115 Subject Guide, Chapter 12.

34. In the Poole model, if both IS and LM shocks are present, an interest rate target will perfectly insulate output from which shocks?

IS shocks. LM shocks. Both IS and LM shocks. Neither IS nor LM shocks.

Correct Answer: B.

An interest rate target works by adjusting the money supply to keep the interest rate constant. This policy perfectly offsets any shocks originating in the money market (LM shocks), preventing them from affecting the interest rate and thus from being transmitted to the goods market and output. However, this same policy will fully accommodate any shocks from the goods market (IS shocks), leading to maximum output volatility from that source.

Source: Poole (1970).

35. The term 'multiplicative uncertainty' is a synonym for:

Parameter uncertainty. Additive uncertainty. Data uncertainty. Model uncertainty.

Correct Answer: A.

Parameter uncertainty is often called multiplicative uncertainty because in a model like \(y = gX\), the uncertain parameter `g` multiplies the policy instrument `X`. This contrasts with additive uncertainty, where a shock term is added to the equation.

Source: EC3115 Subject Guide, Chapter 12.

36. If the correlation between the policy multiplier `a` and the additive shock `u` is positive (\(\rho > 0\)), Brainard (1967) shows that it may be optimal for the policymaker to:

Always be more aggressive. Ignore the correlation. Move the policy instrument in the 'wrong' direction to reduce variance. Set the policy instrument to zero.

Correct Answer: C.

A positive correlation means that when the policy is unexpectedly potent (high `a`), the economy is also likely to be hit by a positive shock (high `u`). If the goal is to raise output, an aggressive policy risks a massive overshoot. To counteract this, the policymaker can exploit the correlation. By moving the policy instrument in the 'wrong' direction (e.g., a contractionary move when the goal is expansionary), the policymaker can reduce the overall variance of the outcome. This is a counter-intuitive but important result showing that correlation between uncertainties can be exploited for stabilization.

Source: Brainard (1967), 'Uncertainty and the Effectiveness of Policy'.

37. The empirical work by Aruoba (2008) on data revisions is important for policymaking because it suggests that:

Policymakers can trust initial data releases. Economic data has become more accurate over time. Data revisions are random and can be safely ignored. The 'real-time' data that policymakers use is subject to systematic biases and predictable errors.

Correct Answer: D.

Aruoba's findings—that revisions are biased, large, and predictable—directly challenge the notion that initial data is reliable or that revisions are pure 'news'. This implies that policymakers are operating in an environment of significant data uncertainty where the initial picture of the economy is flawed in systematic ways. This complicates policymaking, as decisions must be made based on data that is known to be imperfect and subject to predictable change.

Source: Aruoba (2008).

38. In the Poole model, if the LM curve is vertical (money demand has zero interest elasticity), what is the optimal policy instrument?

Money supply targeting. Interest rate targeting. It is impossible to determine. The two instruments are equivalent.

Correct Answer: A.

A vertical LM curve means that output is determined solely by the real money supply. In this case, targeting the money supply gives the central bank direct control over the LM curve's position and therefore direct control over output. Any IS shocks would only change the interest rate but not output. Interest rate targeting would be completely ineffective, as changing the money supply would not move the interest rate at all.

Source: Poole (1970).

39. The breakdown of certainty equivalence due to parameter uncertainty implies that the separation principle no longer holds. What is the separation principle in this context?

The separation of monetary and fiscal policy. The ability to first determine the desired path of the target variable and then separately calculate the instrument settings to achieve it. The separation of the central bank from political influence. The separation of data collection from policy decisions.

Correct Answer: B.

Under certainty equivalence, the policymaker's problem can be separated into two stages: first, decide the optimal path for the target (e.g., close the gap completely); second, calculate the instrument setting needed to achieve that path based on expected values. When parameter uncertainty exists, this separation is not possible. The choice of the instrument setting itself influences the uncertainty (variance) of the outcome, so the decision about the instrument and the desired properties of the outcome (mean vs. variance) must be made simultaneously.

Source: General concept related to Theil's work and certainty equivalence.

40. Which of the following best summarizes the difference between 'news' and 'noise' in data revisions?

'News' is a large revision, while 'noise' is a small revision. 'News' refers to revisions in GDP, while 'noise' refers to revisions in monetary aggregates. 'News' is an unpredictable revision reflecting new information, while 'noise' is a predictable revision reflecting measurement error in the initial announcement. 'News' is a revision from the government, while 'noise' is a revision from private forecasters.

Correct Answer: C.

This is the core distinction. 'News' represents a rational forecast error; the initial announcement was the best possible forecast, and the revision incorporates new information that was fundamentally unknowable at the time. 'Noise' implies the initial announcement was flawed; it was the true value plus a measurement error. This error can often be predicted, meaning the revision (which corrects the error) is also predictable.

Source: Aruoba (2008); EC3115 Subject Guide, Chapter 12.

41. In the Poole model, if the IS curve is vertical (investment and consumption are completely interest-inelastic), what is the optimal policy instrument?

The choice of instrument is irrelevant for output stabilization. Money supply targeting. Interest rate targeting. Fiscal policy.

Correct Answer: A.

If the IS curve is vertical, the level of output is independent of the interest rate. Monetary policy, which works by changing the interest rate to influence aggregate demand, becomes completely ineffective at controlling output. Neither targeting the money supply (which changes the interest rate) nor targeting the interest rate directly will have any effect on output. Therefore, from the perspective of output stabilization, the choice is irrelevant as neither instrument works.

Source: Poole (1970).

42. A central bank that is concerned about parameter uncertainty might prefer which of the following policy frameworks?

A fixed money growth rule (k-percent rule). A 'cold turkey' approach to disinflation. A policy of responding aggressively to all data releases. A gradualist approach, making small adjustments to policy rates over time.

Correct Answer: D.

A gradualist approach, also known as interest rate smoothing, is the practical application of Brainard conservatism. By making small, incremental changes, the central bank can learn about the effects of its policy and the state of the economy while minimizing the risk of a large policy error that could result from an aggressive move based on an uncertain model.

Source: EC3115 Subject Guide, Chapter 12.

43. What does it mean for a central bank to have a quadratic loss function, e.g., \(L = (y - y^*)^2\)?

It only cares about negative deviations from the target. It dislikes positive and negative deviations from the target equally. It has a linear preference for output. It is risk-neutral.

Correct Answer: B.

The quadratic (squared) term means that the loss increases with the square of the deviation from the target \(y^*\). Because the deviation is squared, a negative deviation (e.g., -2) results in the same loss as a positive deviation of the same magnitude (e.g., +2). This implies a symmetric preference for being at the target, where both overshooting and undershooting are considered equally undesirable.

Source: EC3115 Subject Guide, Chapter 12.

44. In the Poole model, if the central bank chooses to target the interest rate, the LM curve effectively becomes:

Vertical. Upward sloping. Horizontal. Identical to the IS curve.

Correct Answer: C.

When the central bank targets the interest rate, it commits to supplying whatever amount of money is demanded at that rate. This means the interest rate is fixed at the target level, regardless of the level of income. In an IS-LM diagram where the interest rate is on the vertical axis, a fixed interest rate is represented by a horizontal line. The LM curve becomes effectively horizontal at the target rate.

Source: Poole (1970); EC3115 Lecture Slides, Unit L.

45. The presence of parameter uncertainty:

Complicates policy design by introducing a trade-off between the mean and variance of the target variable. Simplifies policy design by allowing the central bank to ignore additive shocks. Makes monetary policy completely ineffective. Proves that fiscal policy is always superior.

Correct Answer: A.

This is the fundamental complication introduced by parameter uncertainty. Unlike additive uncertainty, where policy only affects the mean of the outcome, parameter uncertainty means policy affects both the mean and the variance. The central bank must therefore trade off its desire to move the mean to its target level against its desire to keep the variance low. This trade-off is the source of policy conservatism.

Source: Brainard (1967).

46. If data revisions are found to be correlated with the initial data announcement, this is evidence of:

'News'. A well-behaved revision process. A rational forecast by the statistical agency. 'Noise'.

Correct Answer: D.

Under the 'noise' hypothesis, the initial announcement \(y^i\) is the true value \(y^f\) plus an error \(e\), so \(y^i = y^f + e\). The revision is \(-e\). The revision is therefore correlated with the initial announcement. In contrast, under the 'news' hypothesis, the revision is new information and should be uncorrelated with all previously known information, including the initial announcement.

Source: Aruoba (2008).

47. In the Poole model, if the central bank chooses to target the money supply, the LM curve is:

Horizontal. Fixed and upward sloping. Shifting in response to IS shocks. Vertical.

Correct Answer: B.

Targeting the money supply means the central bank fixes the quantity of real money balances, M/P. The standard LM curve, which shows the combinations of income (Y) and interest rate (r) that lead to equilibrium in the money market for a *given* money supply, is upward sloping. By fixing M, the central bank fixes the position of this upward-sloping curve. Shocks will then move the IS curve along this fixed LM curve.

Source: Poole (1970); EC3115 Lecture Slides, Unit L.

48. The certainty equivalence principle is a feature of which class of models?

Models with parameter uncertainty. All stochastic models. Linear-Quadratic (LQ) models with additive uncertainty. Non-linear models.

Correct Answer: C.

The certainty equivalence result, originally developed by Theil and Simon, applies specifically to problems where the model of the economy is linear, the policymaker's objective function is quadratic, and the uncertainty is additive and not affected by the policy instruments. This is often referred to as the Linear-Quadratic framework. Relaxing any of these assumptions (e.g., by introducing parameter uncertainty) generally causes certainty equivalence to fail.

Source: General concept from Theil (1957) and Simon (1956), as discussed in Brainard (1967).

49. A key reason why parameter uncertainty leads to policy caution is that the policymaker is assumed to be:

Risk-averse. Risk-neutral. Risk-loving. Unaware of the uncertainty.

Correct Answer: A.

The cautious response arises because the policymaker is risk-averse, which is captured by the quadratic loss function that penalizes variance. A risk-neutral policymaker would only care about the expected value (the mean) of the outcome and would act aggressively to close the expected gap, ignoring the variance. A risk-averse policymaker, however, is willing to sacrifice some performance in the mean to achieve a less volatile, more predictable outcome.

Source: Brainard (1967); EC3115 Lecture Slides, Unit L.

50. In the Poole model, if the economy is subject to both IS and LM shocks, the optimal policy is to:

Always target the interest rate. Always target the money supply. Use a combination of both instruments. Choose the single instrument that minimizes output variance, depending on the relative magnitude of the shocks.

Correct Answer: D.

Poole's original analysis focused on the choice between two 'pure' strategies: fixing the interest rate or fixing the money supply. The conclusion is that the policymaker should compare the output variance that would result from each strategy and choose the one that produces the smaller variance. This choice depends entirely on the relative sizes of the IS and LM shock variances and the structural parameters of the economy. The paper also briefly considers a combination policy, but the main takeaway is the criterion for choosing between the two simple instruments.

Source: Poole (1970).

EC3115 - Chapter 12 Quiz: Monetary Policy and Data/Parameter Uncertainties