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The Economy is affected by a temporary positive demand shock that lasts two peri...

May 1, 2024

The Economy is affected by a temporary positive demand shock that lasts two periods (1,2), reverting to previous levels of demand from period 3 onwards. The Central Bank is aware of this temporal pattern. Analyse graphically the actions of the stabilizing policy maker up to period 3.

Answer

The central bank will likely increase interest rates during periods 1 and 2 to counteract the inflationary pressure from the positive demand shock and then lower them back in period 3 once the demand reverts to normal.

Solution

Initial Condition: Before the demand shock, the economy is at equilibrium with price level P and output Y at their natural rates

Positive Demand Shock: In periods 1 and 2, the demand shock shifts the aggregate demand curve to the right from AD to AD', leading to a higher price level P' and higher output Y'

Central Bank's Response: To stabilize the economy, the central bank may raise interest rates to reduce investment and consumption, shifting the aggregate demand back towards the left

Reversion of Demand: In period 3, as the demand shock wears off, the aggregate demand curve shifts back to its original position AD. The central bank then lowers interest rates to stimulate the economy back to its natural rate of output Y

Key Concept

Stabilization Policy

Explanation

Stabilization policy involves actions taken by a central bank to counteract macroeconomic fluctuations and maintain price stability and full employment.

Assuming a Loss Function for the policy maker given by: 𝑉=[𝑦−(𝑦𝑒+𝑘)]^2+(𝜋)^2 and that the economy is described by an Expectations Augmented Phillips curve such as: 𝜋=𝜋𝑒+𝛼(𝑦−𝑦𝑒)+𝜀 (with an unbiased random shock 𝜀), demonstrate that under Rational Expectations the following would obtain: 𝜋𝑒>0.

Answer

Under Rational Expectations, it is demonstrated that expected inflation

\pi_e

is greater than zero, \pi_e > 0.

Solution

Loss Function: The policy maker's loss function is given by

V = [y - (y^e + k)]^2 + \pi^2

, where

y

is the actual output,

y^e

is the expected output,

k

is a constant, and

\pi

is the actual inflation rate

Expectations Augmented Phillips Curve: The economy is described by the Expectations Augmented Phillips curve

\pi = \pi^e + \alpha(y - y^e) + \epsilon

, where

\pi^e

is the expected inflation,

\alpha

is a positive constant, and

\epsilon

is an unbiased random shock

Rational Expectations: Under Rational Expectations, agents form expectations such that

y = y^e

and

\epsilon = 0

on average. Therefore, the Expectations Augmented Phillips curve simplifies to

\pi = \pi^e + \alpha(y - y^e)

Positive Demand Shock: A temporary positive demand shock increases actual output above potential output, leading to y > y^e. This implies that \pi > \pi^e due to the positive relationship between output gap

(y - y^e)

and inflation in the Phillips curve

Inflation Expectations: Since the shock is temporary and known to last for two periods, rational agents will anticipate higher inflation in the first two periods. This anticipation leads to a positive expected inflation \pi^e > 0 for those periods

Key Concept

Rational Expectations and Inflation

Explanation

Under Rational Expectations, agents anticipate the effects of a temporary positive demand shock on inflation, leading to positive expected inflation \pi^e > 0 during the shock.

Assuming an open economy, illustrate with a three equations diagram how a permanent positive demand shock would give rise to an under-shooting result in the exchange rate, given the expected reaction of the central bank.

Answer

A permanent positive demand shock in an open economy can lead to an initial overshooting of the exchange rate due to the central bank's reaction, which aims to stabilize prices and output.

Solution

Three Equations Model: The model consists of the following three equations: the IS curve, the Phillips curve, and the exchange rate determination equation

IS Curve: The IS curve represents the equilibrium in the goods market, where output

Y

is determined by domestic demand and net exports, which are affected by the real exchange rate

E

Phillips Curve: The Phillips curve shows the relationship between inflation

\pi

and output

Y

, where higher output leads to higher inflation

Exchange Rate Determination: The exchange rate is determined by the interest rate parity condition, which states that the expected depreciation of the exchange rate is equal to the interest rate differential between the domestic and foreign interest rates

Central Bank Reaction: In response to a permanent positive demand shock, the central bank raises interest rates to prevent inflation, leading to an appreciation of the currency

Exchange Rate Overshooting: Due to the central bank's increase in interest rates, the exchange rate initially appreciates more than what is required for long-term equilibrium, leading to an overshooting. As the economy adjusts, the exchange rate will eventually return to its long-term equilibrium level

Key Concept

Exchange Rate Overshooting

Explanation

Exchange rate overshooting occurs when the exchange rate initially adjusts more than necessary in response to a change in monetary policy or demand shocks, before settling back to its long-term equilibrium level.

Consider the Romer model of endogenous technological progress for two countries – Xanatos and Wakanda. These countries face the identical total output production function: 𝑌=𝐴^0.9𝐿y. In the period 𝑡, countries have the same population (𝐿= 150,000), the same share of population working in R&D sphere (4%), and the same stock of knowledge (𝐴= 200). Other components of the knowledge production function differ. For Xanatos: 𝜃=0.005 ; 𝜆=1 ; 𝜙=0, while for Wakanda: 𝜃=0.05 ; 𝜆=0 ; 𝜙=1. i) Provide a brief economic interpretation of the values for 𝜃,𝜆 and 𝜙 in both countries. ii) Derive the expressions for the growth rate of knowledge and the growth rate of output per capita in two countries. Compute these values for Xanatos and Wakanda in the period 𝑡. Briefly explain the sources of differences in economic growth between two countries.

Key Concept

Interpretation of 𝜃, 𝜆, and 𝜙

Explanation

In the Romer model, 𝜃 represents the effectiveness of research and development (R&D) in creating new knowledge. A higher 𝜃 indicates that each researcher contributes more to the stock of knowledge. 𝜆 represents the contribution of the existing stock of knowledge to the production of new knowledge, with higher values indicating that knowledge is more effectively used to generate further knowledge. 𝜙 represents the spillover effect of knowledge, where a value of 1 indicates full spillover and 0 indicates no spillover. In Xanatos, the low 𝜃 suggests less effective R&D, 𝜆=1 indicates that existing knowledge fully contributes to new knowledge, and 𝜙=0 suggests no spillover effects. In Wakanda, the high 𝜃 indicates highly effective R&D, 𝜆=0 means existing knowledge does not contribute to new knowledge production, and 𝜙=1 suggests full spillover effects.

Key Concept

Growth Rate of Knowledge and Output Per Capita

Explanation

The growth rate of knowledge in the Romer model is determined by the formula

\dot{A}/A = \theta L_A

, where

\dot{A}

is the change in knowledge,

A

is the current stock of knowledge, and

L_A

is the labor in R&D. For output per capita, the growth rate can be derived from the production function

Y=A^{0.9}L_Y

, where

L_Y

is the labor in production. The growth rate of output per capita is then the growth rate of

A

plus the growth rate of

L_Y

minus the growth rate of the total population

L

. For Xanatos, the growth rate of knowledge is

0.005 \times 6000 = 0.03

or 3%, and for Wakanda, it is

0.05 \times 6000 = 0.3

or 30%. The differences in economic growth between the two countries can be attributed to the effectiveness of R&D (𝜃), the contribution of existing knowledge to new knowledge production (𝜆), and the spillover effects of knowledge (𝜙).

1. Consider a government’s dynamic budget constraint in debt to GDP terms. a. Why is this approach sometimes described as analogous to the budget of a household, and why is this analogy deemed to be misleading? b. Why has there been so much concern about the stability or instability of this equation? c. Which rules have been implemented to address these concerns and why have they largely failed to do so? d. Analyse why a consensus on these questions is unlikely to emerge soon.

Answer

The government's dynamic budget constraint in debt to GDP terms is a complex issue that cannot be fully equated to a household budget, and concerns about its stability are linked to the potential macroeconomic implications. Rules implemented to address these concerns have often failed due to the complexity of economic systems and differing economic ideologies, making consensus difficult.

Solution

The government's budget constraint is sometimes compared to a household's budget because both must balance income and expenditure over time. However, this analogy is misleading because governments can influence their income through taxation and monetary policy, and they can borrow over longer time horizons than households

Concerns about the stability of the debt to GDP ratio stem from the fear that high levels of debt may lead to unsustainable interest payments, crowding out of private investment, and potential default. Instability can also affect inflation, exchange rates, and economic growth

Fiscal rules, such as debt brakes and balanced budget amendments, have been implemented to control debt levels. These rules have often failed due to economic shocks, political challenges, and the pro-cyclical nature of such policies that can exacerbate downturns

Consensus on these questions is unlikely due to the complexity of economic systems, the impact of unforeseen events, and the variety of economic theories and ideologies that influence policy decisions

Key Concept

Government vs. Household Budget Analogy

Explanation

The analogy is misleading because governments have more complex and broader economic tools and responsibilities than households.

Key Concept

Stability of Debt to GDP Ratio

Explanation

Stability is crucial for economic confidence, but high debt levels can lead to negative macroeconomic consequences.

Key Concept

Fiscal Rules and Their Effectiveness

Explanation

Fiscal rules aim to ensure sustainable debt levels but often fail due to economic realities and political factors.

Key Concept

Challenges in Reaching Consensus

Explanation

Diverse economic theories and unpredictable events make it difficult to reach a consensus on fiscal policy and debt management.

Consider an economy described by a three equations model augmented by a banking sector. a. A crucial feature that this diagram is meant to represent is that loans generate deposits. How can this be rationalised and is it the case that 100% of the new loans will translate in as many new bank deposits? b. Another crucial feature of the diagram is that both the supply of loans and the supply of reserves are horizontal. How can this be justified? c. Analyse how and why the rationing of credit on the part of commercial banks may trigger a recession in the real side of the economy. d. Assuming that the conditions under c) now hold, can policy measures be put in place to stabilise output?

Answer

Loans create deposits in the banking system, but not necessarily on a one-to-one basis due to leakages. The supply of loans and reserves can be horizontal when banks are willing to lend any amount at the prevailing interest rate, and central banks supply reserves as needed. Credit rationing can lead to a recession by restricting investment and consumption. Policy measures such as monetary or fiscal interventions can be implemented to stabilize output.

Solution

When a bank issues a loan, it creates a deposit in the borrower's account, which increases the money supply. However, not 100% of new loans translate into new deposits due to potential leakages such as cash withdrawals or repayment of existing loans

The supply of loans is horizontal when banks are willing to lend more at the prevailing interest rate, assuming borrowers are creditworthy. The supply of reserves is horizontal when the central bank is committed to providing as many reserves as banks need at the target interest rate

Credit rationing occurs when banks limit the amount of loans, which can lead to a decrease in investment and consumption, slowing down economic activity and potentially triggering a recession

To stabilize output, central banks can lower interest rates or provide more liquidity, and governments can increase spending or cut taxes to stimulate demand

Key Concept

Endogenous money creation

Explanation

The process by which banks create money through lending is known as endogenous money creation.

Key Concept

Horizontal supply of loans and reserves

Explanation

The horizontal supply indicates that banks and central banks are ready to supply additional loans and reserves at the current interest rate.

Key Concept

Credit rationing and economic activity

Explanation

Credit rationing restricts the flow of funds to businesses and consumers, which can reduce investment and consumption, leading to a recession.

Key Concept

Stabilization policies

Explanation

Monetary and fiscal policies can be used to influence economic activity and stabilize output in the face of credit rationing.

Consider a Dynamic Stochastic General Equilibrium (DSGE) model of the economy which is sometimes also known as the new consensus model. a. For this to be the case which of its theoretical features can be said to be new classical? b. Which of its theoretical features can be said to be new Keynesian? c. Assess why the three equations model may not be a sufficiently close representation of the DSGE one.

Answer

The theoretical features of the DSGE model that are new classical include rational expectations and market clearing, while new Keynesian features include price stickiness and imperfect competition. The three equations model may not be a sufficiently close representation of the DSGE model due to its simplified assumptions and lack of microfoundations.

Solution

New Classical Features: The DSGE model incorporates rational expectations, where agents form expectations about the future in a way that is consistent with the model itself. It also assumes that markets clear, meaning that supply equals demand in every market

New Keynesian Features: The DSGE model includes elements like price stickiness, which means that prices do not adjust instantly to changes in supply and demand, and imperfect competition, where firms have some power to set prices above marginal cost

Limitations of the Three Equations Model: The three equations model, typically consisting of an IS curve, a Phillips curve, and a Taylor rule for monetary policy, is a simplified representation that lacks the detailed microfoundations of a DSGE model. It may not capture the full range of economic dynamics and agent behaviors, such as heterogeneous agents and sector-specific shocks

Key Concept

New Classical vs. New Keynesian Features in DSGE Models

Explanation

New classical features emphasize rational expectations and market clearing, while new Keynesian features focus on price stickiness and imperfect competition. The three equations model is a simplified macroeconomic framework that may not capture the complexity of a DSGE model.

Consider the Fisher model of intertemporal consumption. Assume a consumer lives for two periods (𝑡 and 𝑡+1), does not have any initial endowment and leaves no inheritance. Her utility function is represented by 𝑈=ln𝐶𝑡+𝛽ln𝐶𝑡+1, which is maximized subject to the lifetime budget constraint. Assume that due to credit market imperfections, the consumer faces a borrowing constraint: 𝐶𝑡≤ 𝑌𝑡. a. Provide a brief economic interpretation of this borrowing constraint and draw a graph of the consumer’s budget constraint. b. What is the difference between the cases of binding and non-binding borrowing constraint? Describe the optimal intertemporal consumption bundle in case the borrowing constraint is binding. Provide an illustration. c. What can be said about the magnitude of the marginal propensity to consume in case of a binding borrowing constraint, and how it might influence the effectiveness of macroeconomic policy? d. Write down the Euler equation for the given consumer’s utility function and explain if it holds in case of a binding borrowing constraint.

Answer

The borrowing constraint implies that the consumer cannot spend more than their current income in the first period. In the case of a binding borrowing constraint, the consumer spends all of their first-period income on consumption, and the marginal propensity to consume is one. The Euler equation describes the optimal consumption path over time but does not hold if the borrowing constraint is binding.

Solution

Economic interpretation of the borrowing constraint: The borrowing constraint,

C_t \leq Y_t

, means that the consumer cannot borrow against future income to finance current consumption. This reflects credit market imperfections where lenders are not willing to lend to the consumer beyond their current income due to risks such as default

Difference between binding and non-binding borrowing constraints: A borrowing constraint is binding if the consumer's optimal consumption choice without the constraint would have led to C_t > Y_t. In this case, the consumer is forced to consume exactly their income in the first period,

C_t = Y_t

. If the constraint is non-binding, the consumer can smooth consumption over time according to their preferences and the interest rate. The optimal intertemporal consumption bundle when the constraint is binding is at the point where the consumer spends all their first-period income on consumption, and the second-period consumption is financed by the income of the second period

Marginal propensity to consume under a binding borrowing constraint: When the borrowing constraint is binding, the marginal propensity to consume out of current income is one, as the consumer spends their entire income on consumption. This high marginal propensity to consume can amplify the effects of fiscal policy, as an increase in income would directly increase consumption. However, monetary policy may be less effective if it aims to stimulate borrowing and investment, as the constraint prevents borrowing

Euler equation and its validity under a binding borrowing constraint: The Euler equation for the given utility function is derived from the first-order conditions for utility maximization and is given by

\frac{1}{C_t} = \beta (1+r) \frac{1}{C_{t+1}}

, where

r

is the interest rate. This equation implies that the marginal rate of substitution between present and future consumption equals the gross interest rate. However, if the borrowing constraint is binding, the consumer cannot optimize intertemporally as described by the Euler equation, and thus it does not hold

Key Concept

Borrowing Constraint

Explanation

A borrowing constraint limits the consumer's ability to finance current consumption by borrowing against future income, which can alter the optimal consumption path and affect the effectiveness of macroeconomic policies.

Key Concept

Binding vs. Non-Binding Constraints

Explanation

A binding borrowing constraint forces the consumer to consume their entire current income, while a non-binding constraint allows for consumption smoothing based on preferences and interest rates.

Key Concept

Marginal Propensity to Consume

Explanation

Under a binding borrowing constraint, the marginal propensity to consume is one, which can influence the effectiveness of fiscal policy and potentially reduce the effectiveness of monetary policy aimed at stimulating borrowing.

Key Concept

Euler Equation

Explanation

The Euler equation describes the optimal intertemporal consumption path, but it does not apply when a borrowing constraint is binding, as the consumer cannot optimize consumption between periods.

Consider a representative-agent rational-expectations model of the economy. a. Analyse why dissatisfaction has grown as to the ability of this class of models structurally to explain key features of the macro-economy. b. Does Complexity theory provide any better answer? c. Does Post-Keynesian theory provide any better answer?

Answer

Dissatisfaction with representative-agent rational-expectations models has grown due to their inability to account for heterogeneity and financial frictions, among other limitations. Complexity theory offers insights into the dynamic interactions and emergent properties of the macroeconomy, while Post-Keynesian theory emphasizes the role of uncertainty, non-neutrality of money, and effective demand.

Solution

Dissatisfaction with representative-agent rational-expectations models: These models assume a single representative agent with rational expectations, which oversimplifies the diversity of agents and their expectations in the real economy. They often fail to capture key macroeconomic phenomena such as financial crises, persistent unemployment, and the distributional effects of economic policies

Complexity theory's contribution: Complexity theory considers the economy as a complex adaptive system with heterogeneous agents and institutions. It allows for the study of out-of-equilibrium dynamics, network effects, and the emergence of macroeconomic patterns from micro-level interactions, potentially providing a richer understanding of economic phenomena

Post-Keynesian theory's contribution: Post-Keynesian theory focuses on the role of uncertainty, the non-neutrality of money, and the principle of effective demand. It challenges the notion of equilibrium and rational expectations, emphasizing instead the importance of historical time, institutions, and the influence of aggregate demand on output and employment

Key Concept

Limitations of representative-agent rational-expectations models

Explanation

These models are criticized for their inability to explain complex economic phenomena due to their simplifying assumptions about agent behavior and market dynamics.

Key Concept

Complexity theory in macroeconomics

Explanation

Complexity theory provides a framework for understanding the economy as an evolving system of diverse, interacting agents, which may offer better explanations for macroeconomic patterns and crises.

Key Concept

Post-Keynesian theory in macroeconomics

Explanation

Post-Keynesian theory offers an alternative view that incorporates uncertainty, the endogeneity of money, and the impact of demand on economic activity, challenging traditional rational-expectations models.