Title: oxford / 301 macroeconomics

Front: fisher equation

Front: real exchange rate
Back: [latex]$$Q = \frac{E P_f }{P_h}$$ [/latex]
Q = (price of japanese good in £)/(price of UK goods)
Units: [uk good / japanese good]
E = nominal exchange rate = the price of yen = the number of pounds you need to buy a yen [£/Yen]
P_f = price level in Japan [yen / japanese good]
P_h = price level in the Uk [£/UK good].
Q is therefore in [UK good / Japanese good]
Q is the "real price" of japanese goods = how many UK cars needed to buy japanese cars?
Q↑ = depreciation in the real exchange rate = improvement in UK price competitiveness

Front: decomposing growth rates

Front: IS-PC-MR model, graphical representation and effect of a positive inflation shock
Back: With a lagged IS curve and an unforeseen shock

Front: IS curve and equation

Front: PC curve and equation

Front: MR curve and equation

Front: nominal exchange rate
Back: nominal exchange rate:
E = (units of home currency)/(units of foreign currency)
Think of it as the price of one unit of foreign currency, in terms of home currency.
e.g. E = the price of yen = the number of pounds you need to buy a yen (£/Yen)
E↑ is a depreciation of the nominal exchange rate

Front: uncovered interest parity
Back: Suppose there is international capital mobility. At any time, investors can decide whether to (a) invest in bonds in the home currency or (b) buy foreign currency, invest in bonds in the foreign currency, and later buy home currency.
[latex]
$$
\begin{aligned}
\pounds X (1+i_t) &= \frac{\pounds X}{e_t} ({1+i^*_t}) e_{t+1}^E \\
(1+i^*_t) \cdot e^E_{t+1} &= (1+i_t) \cdot e_t \\
e^E_{t+1} - e_t &= i_t \cdot e_t - i^*_t \cdot e^E_{t+1} \\
\frac{e^E_{t+1} - e_t}{e_t} &= i_t - i^*_t \cdot \frac{e^E_{t+1}}{e_t}
\end{aligned}
$$
Now we make an approximation:
$$
\frac{e^E_{t+1} - e_t}{e_t} = i_t - i^*_t \cdot \frac{e^E_{t+1}}{e_t} \approx
i_t - i^*_t.
$$
UIP:
$${\bf \frac{e^E_{t+1} - e_t}{e_t} = i_t - i^*_t.}$$
Now we make a second approximation:
$$
\frac{e^E_{t+1} - e_t}{e_t} \approx
\ln e_{t+1}^E-\ln e_t
$$
UIP (log form):
$${\bf i_t - i^*_t =\ln e_{t+1}^E-\ln e_t}$$
The advantage is that we can now represent the UIP as a 45 degree line in $e_t, i_t$-space. \\
\\
We can convert the UIP (log form) into real form:
$$r_t-r^* = \ln Q^E_{t+1} - \ln Q_t$$
Where $Q$ is the real exchange rate.
[/latex]

Front: UIP curve

Front: summary equation of IS-PC-MR model
Back: assume adaptive expectations PC and a 1-period lag in montary policy transmission:
We can derive:
and thus:
The larger a, the more the CB should raise rates. The effect of the other parameters is more ambiguous.

Front: IS-PC-MR extensions
Back: A few standard extensions:
* forward-looking CB
* rational inflation expectations (PC)
* sticky prices (PC)
* open economy

Front: inflation bias
Back: Inflation bias shifts the MR curve to the right.
Impact of y^T > y\bar depends on whether expectations adaptive or rational and whether CB loss function static or dynamic.

Front: WS-PS model of the labour market
Back: When WS != PS, inflation changes:

Front: rational expectations and full price flexibility
Back: Under RE and full price flexibility, we get a vertical Phillips curve.
Thus the path of the economy is A→  B→  A. There are no multi-period deviations from Y^E , a conclusion which is represented by a vertical Phillips curve.
Under these assumptions, as long as the CB’s inflation target is credible, the CB need never actually change its interest rate.

Front: Phillips Curve microfoundations
Back: Because of full price flexibility and imperfect competition in the labour market, inflation depends on the output gap.
To see the relationship between inflation and output, suppose Y increases to Y^H because of an exogenous shock.
In the first period, the price level is still P^E, and unions set W=W^A , in order to target point A. However, firms then set P=P^B, which successfully brings the labour market to point B. Prices have now increased by P^B-P^E, so there is positive inflation. This is the rationale behind the positive parameter α in the Phillips curve.

Front: The NKPC
Back: Rational expectations
Sticky prices
lead to the NKPC:
where:
delta is the discount rate
lambda is the proportion of firms that are able to change their prices each period
alpha is a positive parameter
Assuming no discounting, we get:

Front: derivation of output-gap statement of NKPC
Back: We assume that firms do not discount the future, i.e. the discount factor is equal to 1.

Front: Zero Lower Bound
Back: The nominal interest rate has a zero lower bound (ZLB): it cannot go much below zero. This is because of the existence of cash. If the nominal interest rate is negative, people will start to keep money in cash.
Therefore, the real interest rate also has a lower bound. By the Fisher equation:
r=i-π
the real interest rate r cannot go below -π.

Front: Deflationary spiral at the ZLB
Back: assume a 1-period lag in monetary transmission and that the shock is foreseen

Front: Quantiative Easing
Back: Quantitative easing is the name given to asset purchases by the central bank, like the ones pursued by central banks around the world during the Great Recession.
i.e. the CB replaces cash in its balance sheet with assets.
Examples of assets bought by CBs:
government bonds
bonds issued by private companies

Front: forward guidance
Back: forward guidance = the CB publishes the interest rate path it intends to implement.
By the expectations hypothesis, expectations about future short-term rates affects current long-term rates. This increases investment.
We might distinguish two types of forward guidance:
* "loss function clarification"
* "promise to deviate"
Clarification: only effective if agents had biased expectations of the CB's behaviour.
Promise to deviate: if it were credible, this would have an effect even on unbiased agent. But it is time inconsistent. CB will prefer to set r=r\bar (i.e. to target \pi=\pi\bar) once the shock is passed.

Front: define balanced growth path
Back: Y/K is constant

Front: the solow model
Back: Capital Growth at any time:
[latex]
$$\frac{K_{t+1}-K_t}{K_t} = -d +sA L^{1-\alpha} K_t^{\alpha-1}$$
[/latex]
Easy to veryify that this is positive iff k_t is less than its long-run steady-state level.

Front: Solow-Swan model
Back: Express steady-state in terms of capital per effective worker

Front: Solow-Swan model with exogenous technology growth

Front: Labour- and capital-augmenting technological change
Back: A production function is capital-augmenting iff
for all A, K, L: F(K,L,A)=F(AK,L)
A production function is labour-augmenting iff
for all A, K, L: F(K,L,A)=F(K,AL)

Front: deficit bias
Back: deficit bias is the tendency for budget deficits to rise in recessions, but not to fall in a sufficiently offsetting way in booms.
causes:
* over-ambitious output target, i.e. seeking to achieve unemployment below the equilibrium rate (perhaps for political economy reasons)
* over-optimistic growth forecasts
* intergenerational conflict

Front: Two remedies to defict bias
Back: 1. Fiscal policy rules
2. Fiscal policy councils

Front: deriving the prudent fiscal policy rule

Front: the prudent fiscal policy rule
Back: Where the superscript P refers to the long-run or permanent value.
implications:
1. Any permanent increase in government expenditure, such as a rise in long-run government pension obligations, should be financed through a rise in taxation.
2. Any temporary increase in government expenditure, such as rising government transfers in a recession, should be financed through borrowing
Comments:
1. Constant tax share = smoothing taxation over time = analogous to consumption smoothing.
2. Why constant share? Because tax distortion grows more than linearly with the tax.

Front: fiscal policy councils
Back: It is the fiscal policy council's mandate to
- guard against deficit bias
by
- providing independent forecasts of the evolution of the publica finances
- calling the government to account when they tax and spending plans are unsustainable.
The mandates of fiscal policy councils, starting with the narrowest:
1. To produce forecasts for growth, the output gap and the public finances on which the government's fiscal decisions conforming to their targets must be made (e.g. the UK's Office for Budget Responsibility)
2. To carry out positive policy analysis - i.e. to assess the fiscal cost of different policies (e.g. the US CBO)
3. To make normative recommendations based on the government's stated economic objectives - i.e. to actively engage in public debate about fiscal policy decisions (e.g. the Swedish fiscal policy council)

Front: raising taxes vs cutting spending in a simple keynesian multiplier model

Front: the government budget identity

Front: primary vs actual deficit

Front: deriving the simple keynesian multiplier

Front: output-gap statement of NKPC

Front: summary of demand side

Front: summary of supply side

Front: Summary of MR

Front: QE transmission channels

Front: QE 1

Front: QE 2

Front: QE 3

Front: QE 4

Front: QE 5

Front: risks of QE
Back: 1. CB independence and credibility
2. Inflation expectations
3. Financial cycle
4. Excess reserves
5. Exit

Front: QE risk 1

Front: QE risk 2

Front: QE Risk 3

Front: QE risk 4

Front: QE risk 5

Front: open economy IS curve

Front: AD-ERU model

Front: RX curve

Front: inflation shock in the open economy

Front: varieties of philipps curve

Front: the important variables in IS-PC-MR exercises
Back: 1. PC forward or backward-looking? Prices sticky or not?
2. Is there a lag in the effect of r_t on y_t?
3. Is the shock foreseen or unexpected?

Front: ricardian equivalence df
Back: The Ricardian equivalence theorem states that government bonds and lump-sum taxes are equivalent means to finance government spending. Thus, a lump-sum tax cut financed by the issuance of one-year government bonds would not affect consumption.
Other fields (not shown on cards):
notes: Source: The New Palgrave Dictionary of Economics

Front: euler equation
Back: Describes optimal consumption smoothing over 2 periods when Utility is the Log of consumption
(r is the interest rate
rho is the rate of time preference of the households)

Front: expectations hypothesis
Back: The expectations hypothesis is the proposition that the long-term rate is determined purely by current and future expected short-term rates

Front: ricardian equivalence intuition
Back: if HHs and governments borrow at the same rate, then when the govt borrows, the intertemporal budget constraint of the HHs is unchanged. So consumption must be unchanged.

Front: intertemporal consumption summary
Back: Intertemporal budget constraint:
[$$]\sum_{t=0}^{T-1} c_t \frac{1}{(1+r)^t} \leq a_0 + \sum_{t=0}^{T-1} y_t \frac{1}{(1+r)^t}[/$$]
There is no explicit solution to this problem in general. But, if HHs and govt borrow at same rate r, we can see that the intertemporal budget constraint of households is unaffected by a lump sum tax cut financed by govt borrowing. So this is enough to get Ricardian equivalence!
If we add assumptions, we can derive explicit expressions for consumption:

Front: Permanent income hypothesis
Back: Special case of intertemporal consumption when rho = r. (the rate of time preference equals the rate of interest).