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Macroeconomics > 2+3 - Elements of Equilibrium > Flashcards

2+3 - Elements of Equilibrium Flashcards

1
Q

What Are DSGE Models?

A
  • Dynamic, i.e., inter-temporal aspects of individual decision making are taken into account.
  • Stochastic, i.e., the presence of uncertainty is modeled.
  • General Equilibrium, i.e., all individual plans are mutually consistent.
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2
Q

Why Are Micro-Founded Structural Models Useful?

A
  • Micro-founded structural models permit utility-based policy analysis in a way that takes the Lucas critique into account.
  • Of course, normative implications are only useful if the underlying models are empirically relevant.
  • Models can be used as a lens to look at the data.
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3
Q

What is the problem of non-micro-founded models?

A

Correlations in the data, without a working theory of how people may react to policy changes, cannot be used to guide economic policy.

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4
Q

What is the Lucas’ critique?

A

Correlations among macroeconomic aggregates result from decisions by individuals. Government policies are an important part of the economic environment in which those decisions are taken. If policy changes, the environment changes and as a result correlations among macroeconomic aggregates are also altered.

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5
Q

What are sᵗ and sₜ?

A
  • sₜ: Realization of stochastic event,
    sₜ ∈ S.
    Example: S = {sunshine, rain}
  • sᵗ: State of the world,
    sᵗ = [s₀, s₁, …, sₜ].
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6
Q

What is E₀?

A

E₀ is the expected value conditional on the state of the world at time t = 0. It is a probability weighted sum.

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7
Q

What does βᵗ stand for?

A
  • t…simply an exponent of the parameter β
  • β ≡ 1 /( 1+ρ )
  • ρ is the time preference rate.
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8
Q

What is Cₜ?

A

Consumption (Quantity consumed of the single good available in the economy.)

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9
Q

What is Nₜ?

A

Nₜ: Labor, hours of work

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10
Q

What is the households’ objective?

A

Maximize expected utility over all time, as a function of labor and consumption

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11
Q

What is Pₜ?

A

Price of the consumption good

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12
Q

What is Wₜ?

A

Nominal wage

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13
Q

What is Bₜ?

A
  • Quantity of one-period, nominally riskless discount bonds purchased in period t and maturing in period t+1
  • Each bond pays one unit of money at maturity
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14
Q

What is Qₜ?

A

Bond price

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15
Q

What is Tₜ?

A

lump-sum additions or subtractions to period income (e.g., taxes, dividend, etc.)

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16
Q

What is the household’s budget?

A

PₜCₜ + QₜBₜ ≤ Bₜ₋₁ +WₜNₜ - Tₜ,

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17
Q

What is the No Ponzi-game condition for the household and what does it mean?

A

Intuitively, this means that in present-value terms, the agent cannot engage in borrowing and lending so that his “terminal asset holdings” are negative, since this means that he would borrow and not pay back

A no-Ponzi-game condition is a constraint that prevents overaccumulation of debt.

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18
Q

What is the household’s optimization problem?

A
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19
Q

What is the economic interpretation of parameter σ?

A

coefficient of relative risk aversion:

The parameter σ ≥ 0 determines the curvature of the utility of consumption, it is consumption smoothing.

The higher σ, the higher the risk aversion.

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20
Q

What is the economic interpretation of parameter φ?

A

degree of convexity of labor disutility:

Parameter f is the inverse (Frisch) labor supply elasticity. In other words, f determines the curvature of the disutility of labor.

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21
Q

What is πₜ(sₜ)?

A

probability of a specific state of the world

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22
Q

What does λ represent in the lagrangian function?

A

λ = marginal value of marginal relaxation of a constraint

-> e.g. household gets one unit of money for free > how does that affect the utility maximization problem?

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23
Q

What is the problem of policy analysis that is purely based on correlations observed in the data?

A
  • A statistical link between macroeconomic variables is always the result of the decisions of individuals and thus depends on the economic environment.
  • Once the environment changes, also the decisions and thereby the statistical relationship can change. As government policies are an important part of the economic environment, a change in economic policy can alter the decision making that is reflected in the statistical link.
  • A policy aimed at exploiting an empirically observed relationship can thus be unsuccessful or even harmful, because the relationship can change when the policy is implemented.

(Lucas’s Critique)

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24
Q

Give an example of the problem of policy analysis that is purely based on correlations observed in the data?

A
  • In 1958, Phillips found a negative relationship between inflation & unemployment. Politicians, but also economists, wanted to exploit this apparently stable tradeoff.
  • However, after increasing inflation on purpose, the link vanished and a high inflation rate coexisted with a still high unemployment rate.
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25
Q

What are the main characteristics of a Micro-founded model?

A

The main characteristic of Micro-founded models is that they explicitly model preferences, technology, market structure and frictions under the assumption of structural (“deep”) parameters that are assumed to be policyinvariant.

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26
Q

What is Rₜ?

A

real interest rate, inverse of Q

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27
Q

What is iₜ?

A

nominal interest rate

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28
Q

What is πₜ?

A

inflation rate

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29
Q

What is Aₜ?

A

level of technology

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30
Q

What is Yₜ?

A

output

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31
Q

What is MCₜⁿ?

A

the nominal marginal cost (differentiation of the cost function w.r.t. Y)

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32
Q

What does this equation mean?

A

the goods market equilibrium (=clearing condition)

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33
Q

What does this equation mean?

A

production function

34
Q

What does this equation mean?

A

expression for real marginal cost (relationship between real marginal costs and economic activity)

35
Q

What does this equation mean?

A
  • it is the new IS curve (=represents all combinations of income (Y) and the real interest rate (r) such that the market for goods and services is in equilibrium)
  • equation stems from the log-linear Euler equation (with y instead of c, because in equilibrium, y = c)
  • name derives from the property that it represents that desired investment equals desired saving
36
Q

What does this equation mean?

A

real money demand

37
Q

What is the difference between variables and parameters?

A

Parameters are fixed and variables are variable.

Parameters reflect certain parts of the environment which we believe are constant over time, at least at short to medium horizons. Their values are chosen in accordance with data. Some can be measured directly and some have to be calibrated.

38
Q

What is the difference between exogenous and endogenous variables?

A
  • Exogenous variables are assumed to be determined by forces which are not part of the model, hence, they are exogenous to the model. An example for an exogenous variable from our course is technology (Aₜ).
  • Endogenous variables are determined within the model. The dynamics of the endogenous variables are driven by the exogenous variables.
39
Q

What characterizes the equilibrium of a macroeconomic model?

A

it refers to an intertemporal equilibrium where:

1) All agents behave optimally and
2) All economic plans are competible with each other.

40
Q

Why does yₜ = cₜ always has to hold in equilibrium?

A

Consumption plan of household and production plan of firm are compatible with each other.

41
Q

What does it mean to “determine the equilibrium” or “solve for the equilibrium”?

A

Express all endogenous variables exclusively as functions of the exogenous variables (and parameters).

42
Q

What is -µ?

A

a constant markup

43
Q

What is the difference between real and nominal variables?

A
  • Real variables are expressed in real terms (the effects of the price level are removed), usually in terms of the consumption good, for example, consumption Cₜ, output Yₜ, real interest rate rrₜ, labor Nₜ (expressed in “physical” terms, hours worked).
  • Nominal variables are expressed in monetary terms, for example, nominal wage Wₜ, nominal interest rate iₜ, inflation rate Pₜ, amount of money, Mₜ.
44
Q

What is rrₜ?

A

Real interest rate

45
Q

What is iₜ?

A

nominal interest rate

46
Q

What is Pₜ?

A

inflation rate

47
Q

What is Mₜ?

A

amount of money

48
Q

What is the economic interpretation of 1/σ ?

A

The parameter 1/σ is the intertemporal elasticity of substitution. It is a measure of responsiveness of consumption to the real interest rate, as can be seen from the consumption Euler equation.

49
Q

What is the economic interpretation of parameter β?

A

Parameter 0 < β < 1 is the discount factor of the household. The smaller β, the more impatient is the household, i.e., it values future utility by less, .

50
Q

What is the economic interpretation of parameter ρ?

A

Parameter ρ represents the time preference rate of the household.

It is given by β ≡ 1/(1+ρ) (and log(β) ≈ -ρ).

51
Q

What is the economic interpretation of parameter η?

A

Parameter η denotes the (nominal) interest semielasticity of (real) money demand.

It gives by how much the quantity of money demanded is reduced (increased) by an increase (a reduction) in the nominal interest rate of one percentage point, or 100 basis points.

= effect of a % change in nominal interest rate on money demanded

52
Q

What is the economic interpretation of parameter ϵ?

A

The parameter ϵ > 1 has two interpretations:

  1. It gives the elasticity of substitution between two goods (see definition of the consumption index).
  2. It gives the price elasticity of demand for the individual goods (see firm’s demand constraint).
53
Q

What is the economic interpretation of parameter μ?

A

Parameter μ = log(M) = log( ϵ/(ϵ-1 ) stands for the log mark-up of the firm. In other words, it is the difference between the (log) selling price of the final good and the (log) nominal marginal cost.

54
Q

What is the economic interpretation of parameter θ?

A
  • Parameter θ is the Calvo parameter.
  • it gives the probability in any given period (which is independent of the time elapsed since the last price adjustment) that a firm cannot reset its price. Conversely, (1-θ) gives the probability that a firm will be able to reset its price in any given period.
  • It can also be interpreted as the fraction of firms that keep their prices unchanged.
  • Finally, the average duration of a price is given by 1/(1-θ) .
55
Q

What is an interest rate?

A

An interest rate is defined as the proportion of an amount loaned which a lender charges as interest to the borrower, normally expressed as an annual percentage.

It is the rate a bank or other lender charges to borrow its money, or the rate a bank pays its savers for keeping money in an account.

56
Q

What is difference between nominal and real interest rate?

A
  • A real interest rate is adjusted to remove the effects of inflation and gives the real rate of a bond or loan.
  • A nominal interest rate refers to the interest rate before taking inflation into account.
  • To calculate the real interest rate, you need to subtract the actual or expected rate of inflation from the nominal interest rate.
57
Q

What are bonds?

A
  • Bonds are units of corporate debt issued by companies and securitized as tradeable assets.
  • A bond is referred to as a fixed income instrument since bonds traditionally paid a fixed interest rate (coupon) to debtholders. Variable or floating interest rates are also now quite common.
  • Bonds have maturity dates at which point the principal amount must be paid back in full or risk default.
58
Q

What is the relationship between bonds and interest rates?

A

Bond prices are inversely correlated with interest rates: when rates go up, bond prices fall and vice-versa.

59
Q

What is Ponzi?

A
  • A Ponzi scheme is a fraudulent investing scam promising high rates of return with little risk to investors. The Ponzi scheme generates returns for early investors by acquiring new investors. This is similar to a pyramid scheme in that both are based on using new investors’ funds to pay the earlier backers.
  • Named after Charles Ponzi (Born in 1882 in Parma, Italy): the infamous swindler who payed out returns with other investors’ money. After running a highly profitable and expansive investment scheme, Ponzi was arrested on August 12, 1920, and charged with 86 counts of mail fraud.
60
Q

What is demand for money?

A

In monetary economics, the demand for money is the desired holding of financial assets in the form of money: that is, cash or bank deposits rather than investments.

61
Q

What are dividends?

A
  • Dividends are payments made by publicly-listed companies or funds as a reward to investors for putting their money into the venture. They can be paid as cash or in the form of stock.
  • Announcements of dividend payouts are generally accompanied by a proportional increase or decrease in a company’s stock price.
  • Investors can use models, such as the dividend discount model or Gordon growth model, to find dividend-paying instruments.
62
Q

What is the intuition behind the (consumption) Euler equation?

A

it is the idea that the optimal consumption path must be such that the marginal utility lost from consuming a little less today is exactly the same as the marginal utility gained consuming more tomorrow.

63
Q

What is the time preference rate?

A
  • From neoclassical theory of interest by Irving Fisher
  • the rate of time preference is a parameter in an individual’s utility function: it captures the trade off between consumption today and consumption in the future
  • it is thus exogenous and subjective.
64
Q

What is the difference between bonds and shares?

A

The difference between stocks and bonds is that stocks are shares in the ownership of a business, while bonds are a form of debt that the issuing entity promises to repay at some point in the future.

65
Q

What is a semi-elasticity?

A
  • a percentage change in output is divided by a unit (not percentage) change in input
  • A semi-elasticity (or semielasticity) gives the percentage change in f(x) in terms of a change (not percentage-wise) in x
66
Q

What is consumption smoothing?

A

Consumption smoothing = people’s desire to have a stable path of consumption

People desire to translate their consumption from periods of high income to periods of low income to obtain more stability and predictability.

67
Q

What is the difference between a realization of a stochastic event and the state of the
world (in words)?

A
  • The realization of stochastic event, sₜ, is a particular outcome of a stochastic process
    • S -> sₜ ∈ S
    • e.g. if weather can only be described on whether the sun is shining or if it is raining: S = {sunshine, rain}, where S contains all possible realizations (sunshine or rain).
  • The state of the world, sᵗ, is a vector containing current and all previous realizations of a stochastic event.
    • sᵗ = [s₀, s₁, …, sₜ]
    • the state of the world describes which “path” along a tree of histories was experienced until today.
68
Q

Describe what this formula and its elements mean:

A

Second sum: expectation is a probability-weighted sum of the different possible realizations of the variable.

  • sᵗ denotes the history of realizations up to time period t
  • πₜ(sᵗ) denotes the probability at time t of being in state sₜ
  • discount factor is defined as β = (1 / (1+ρ) , where ρ is the time preference rate
69
Q

Interpret λ an ~λ:

A

The Lagrange multiplier λ reflects the shadow value of a marginal relaxation of the constraint in terms of the objective function.

Here:

  • λₜ, reflects the additional gain in utility in period t, given a relaxation of the budget constraint in period t
  • λ˜ₜ reflects the additional gain in expected discounted utility today, given a relaxation of the constraint in period t
70
Q

What is this equation and what do its components mean?

A

it is the optimal labor supply equation

    • Uₙ,ₜ / U𝒸,ₜ = marginal rate of substitution between work and consumption
  • Wₜ / Pₜ = real wage
71
Q

What information does this equation contain?

A
  • Eₜ …the expectation given the information available in time t, i.e. the realized state at time t.
  • Qₜ / Pₜ …the quantity of consumption goods that one foregoes at time t by purchasing a bond.
  • 1 / (Pₜ₊₁) …the quantity of consumption goods that one can buy at time t + 1 with the payoff of the bond
72
Q

What does this equation show?

A

the equilibrium price of the bond

73
Q

What are frictions that can be included in a model?

A

e.g. Sticky Prices in Monetary DSGE Models

74
Q

What are positive implications from sticky prices in Monetary DSGE Models?

A

Sticky prices imply empirically plausible effects of monetary disturbances for macroeconomic variables of interest

75
Q

What are normative implications from sticky prices in Monetary DSGE Models?

A
  • Poorly designed monetary policy can be in itself a source of unnecessary macroeconomic fluctuations
  • Monetary policy can affect welfare relevant variables in a desirable way
76
Q

What is the difference between positive and normative?

A
  • While positive economics is based on fact and cannot be approved or disapproved, normative economics is based on value judgments.
  • The statements under positive economics can be tested or verified. The statements under normative economics are subjective in nature.
77
Q

What does this definition mean and what could it be useful for?

A

πₜ = inflation

It can help to for example simplify the equation below to

πₜ₊₁

78
Q

What is the main takeaway from this formula?

A

that the real interest rate rₜ is a key player in determiing aggregate demand (=consumption)

rₜ is marked here:

79
Q

What is this?

A

log of the labor supply equation, graph:

  1. the household needs to receive a higher wage in order to work more (x-axis in graph)
  2. if the household can enjoy higher consumption, it means he is wealthier (lines in graph)
80
Q

What is the production function of a typical firm in equilibrium?

A
  • Y = output
  • A = level of technology
  • N = units of labor
81
Q

What does this function represent?

A

costs associated with producing Y

82
Q

How to get MCⁿₜ and what does it mean?

A

Differentiating the costs of production with respect to Y, which yields the nominal marginal costs

Macroeconomics (8 decks)

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