Econonic Growth, Cycles and Policy

The following notes come from the course Economic Growth, Cycles and Policy, held by Prof. Dr. Hans Gersbach at ETH Zurich.

(I spent one semester working for Hans Gersbach at KOF and I couldn't be more enthusiastic: he’s clever, prepared, and very inspiring.)

Please refer to his list of publications to deep dive in the subject.

Index

• Introduction
• Macroeconomic Schools
• IS-LM Model in Closed Economy
• Aggregate Demand and Aggregate Supply Curves
• Control of Interest Rates and Taylor Rule
• Schools of Thought
• Consumption and investment
• The Solow Growth Model
• Money holding: Inflation and Monetary Policy
• Crises in Market Economnies
• IS-LM Model and Open Economy
• Theories of exchange rate determination
• Technical Appendix

1.1 Introduction

Macroeconomics tries to answer some key questions:

• What determines key macroeconomic variables? _(GDP, unemployment, inflation, credit, consumption, interest rate...)
• How can economic policy influence these variables? _(government spending, tax policies, monetary policy, "wage policy"...)
• How can macroeconomic policy and market regulation operate together?
• Do macroeconomic processes show inherent dynamics? (cycles, trend and instabilities)
• Should economic policy focus mainly on long-run growth or on stabilization of the business cycle?

To start answering them, we firstly start with some stylized facts of Macroeconomics:
Note that, if a variable is procyclical, it moves in the same direction as the overall economy.

Some additional common rules of macroeconomic policy, based on consensus, argue that:

• in case of liquidity problems, the central bank should provide liquidity by raising money supply.
• Government spending and investments of infrastructure should not be lowered during recession periods.
• In downturns automatic stabilizer (first responders" to an economic crisis) should work.
• In the long run monetary policy has to focus on price stability (inflation around 2% a year).
• Real wage increases should not exceed productivity growth whem at the sime time the number of employees remain constant.

1.2 Macroeconomic Schools

The following graph shows the evolution of the macroeconomic thought from 1950 till today.

• Keynesians: focus on the short-run. They argue that markets don't always clear and that government intervention is necessary to manage the business cycle.
• New Kenynesians: they introduce microfoundations _(explaining how people behanve and spend) and nominal rigidities (prices and wages don't adjust instantly, which justifies government intervention).

• Classic: they argue that markets are self-correcting and the invisible hand ensures optimal employment in the long run.
• New Classic: Emerged in 1970, they introduced rational expectations, suggesting that because people anticipate government policy, those policies often become ineffective.

• Monetarists: led by Milton Friedman, they argued that changes in the money supply are the main driver of economic fluctuations.
• RBC Economics (Real Business Cycle): they are a subset of New Classical thought. They argue that "cycles" aren't failures of the market, but rather efficient responses to technological shocks or changes in productivity.

2.1. IS-LM Model in Closed Economy

In the long run:

• prices are flexible
• output is ddetermined by factors of production and technology
• unemployment equals its natural rate

In the short run (IS-LM setting):

• prices are fixed (or change slowly)
• oputput is determined by aggregate demand

In equilibrium, money supply equals money demand:

where $L(i,Y)$ is a function representing the liquitidy preferences, $i$ is the interest rate and $p$ the price level.

If we consider $L(i,Y)=kY-hi$ where:

• $\alpha$: Sensitivity of money demand to changes in income ($\frac{\partial L}{\partial Y}>0$).
• $\beta$: Sensitivity of money demand to changes in the interest rate ($\frac{\partial L}{\partial i}<0$).

If we write $M^s=p(\alpha Y-\beta i)$ and solve for $i$:

This yields an upward-sloping LM curve, which represents the positive relation between the interest rate and the output.

In this model:

• the Central Bank (CB) controls money supply
• if output increases, the demand for money increases at any $i$.
• for a fixed supply of money, $i$ must increase to lower the demand for money and maintain equilibrium.

It is also important to distinguish between:

• Movements along the curve: caused by a change in output ($Y$).
• Shifts of the curve: caused by changes in Monetary Policy (the Money Supply).

Indeed, increasing money suppòly leads to:

• increase in demand for money to maintain equilibrium $\to i$ must decrease
• for any level of output $Y$, the corresponding $i$ is lower.

The result is that an increase in the money supply leads the LM curve to shift down:

• $\Delta M^s\to \Delta i=-\frac{\Delta M^s}{p\beta }$ or, equivalently: $\frac{\partial i}{\partial M^s}=-\frac{1}{\beta p}$
• $\Delta i\to \Delta M^s=-p\beta \Delta i$ or, equivalently: $\frac{\partial M^s}{\partial i}=-\beta p$.

Assumptions:

• there is only one good that can be used for consumption or investment
• all demanded goods will be supplied (no rationing of demand).

We then model planned expenditures $E$:

where $C$ is the consumption, $I$ physical investments (not financials!) and $G$ the public spending.

When $E=Y$ planned and effective expenditures are equal and we obtain the IS-curve.

If we consider: $E=Y=cY+I_0-\gamma i+G$, we obtain the following:

Even though the IS-curve is often referred to as the goods market equilibrium condition, this is misleading.
In microeconomics, a market equilibrium balances demand and supply via price adjustments (market clearing condition).
The IS-curve does not reflect endogenous price levels.

Intiuitively, if we consider increase in public spending $G$:

• increase in public spending moves the IS-curve to the right, $Y$ increases.
• the LM-curve remains unchanged
• in the short run, interest rate and outputincrease.

In formulas, if we consider $\Delta G$ and we solve both IS and LM equations simultaneously, from the LM-curve we get:

if we substitute this into the IS-expression:

If we consider $\Delta G$ or, equivalently, we take its partial derivative:

Dividing both sides gives us the Fiscal Policy Multiplier:

• $(1-c)$: represents the how much goes into savings (smaller this is, the bigger the multiplier).
• $\alpha \gamma /\beta$: is the monetary drag.
  • If $\alpha$ is high, income growth creates massive money demand.
  • If $\gamma$ is high, investment is very sensitive to interest rates.
  • If $\beta$ is low, it takes a larger increase in $i$ to balance the money market.

• Central Bank increases money supply by setting lower interest rate at given $Y$.
• The LM-curve shifts downward
• The IS-curve remains unchanged
• $Y$ increases (with $G$ unchanged because exogenous, $I$ increases and $C$ increases) and $i$ declines

• It may be caused by financial crisis, wars, terror attacks or whatever
• Households consume less and save more of given income
• the IS-curve odes leftward
• LM-curve remains unchanged assuming, for simplicity, that the demand for money does not change
• $Y$ and $i$ decline.

Possible counter-measures to stabilize $Y$:

• Expansive fiscal policy can shift the IS-curve to initial position
• Easing of monetary policy implies downard shift of LM-curve

2.2. Aggregate Demand and Aggregate Supply Curves

So far we've been using the IS-LM model to analyze the short-run dynamics. However, a change in price level would shift the LM-curve and therefore affects the output.
The (aggregate demand) AD-curve describes the relationship between price and output.

On the other hand, we can model the short-run aggregate supply curve with an upward slope (given by sticky wages and sticky costs).

We now give an example of complete adjustment and we see what happend with a reduction of the government spending.

Firstly, a reduction in $G$ shifts both IS and AD-curves left.

In the short-equilibrium, $Y$ is lower than the initial-natural value $\bar{Y}$.

Thefore, aggregate supply moves down and we see a gradual adjustment of pcises, leading to a downward-shift of the LM-curve that, finally, brings the system back to $\bar{Y}$.

In reality, downward price and wage adjustments are difficult (see for example, the Greek crisis in 2010-2016):

• very long wage contract make them hard to re-negotiate
• resistance of particular groups of employees.

In the case of Greece:

• costs were also partly determined by international markets due to the import
• governments has to rely too much on increasing valued added-takex that leads to an increase in prices.

2.3. Control of Interest Rates and Taylor Rule

Models with LM-curve assume that the CB uses the money supply as an instrument, therefore $i$ will determined endogenously by the equilibrium.
In reality, CB uses short-term interest rates as their policy instruments (rather than the money supply).

The main advantage of targeting interest rating versus money supply is that, in the second case, the difference between fluctuating demand and stable siupply would lead to strongly functuating interest rates.
Nowadays CB counterbalance fluctuations in money demand by adapting the money supply to maintain the short-term interest rate at the targeted level.

CB influences short-terminterest rates $i_0,i_1,i_2...$.

A risk-neutral investors must be indifferent between:

• make a long-term investment with interest rate $i_L$
• make short-term investments in each period $t$ at interest rate $i_t$ (with $i_t^e$ denoting the expected interest rate)

But, in practice:

where ${\tau }_{n-1,n}^P$ denotes the positive term premium.

In this way, by influencing the short-term nominal interest rates, the CB can also influence the long-term ones.

3. Schools of Thought

The following basic RBC-model starts with the following assumptions:

• an infinitely long-living household/agent maximizes the expected value of

with respect to the intertemporal budget restriction, where $u_t$ represents the utility in period $t$ and $0<\delta <1$ the discount factor.

• a representative firm maximizes profits, given its production function.
• there exist no frictions (no price rigidities, no externalities, no asymmetric info, no public goods...)

The aggregate production function is then:

• $Y_t$ aggregate output
• $A_t$ measure for the efficeny of labor (stochastic), example: $\ln A_t=\bar{A}+\rho {ϵ}_{t-1}+{ϵ}_t$, with $ϵ\sim N(0,{\sigma }^2)$, where $\rho$ describes the persistence of the shock.
• $K_t$ capital
• $L_t$ labor input
• $\alpha$ share of physical capital

Intuition: the stochastic component A_ induce business cycles.

$A_t$ is then a measure fo the efficiency of labor over time and relative to capital. It's a cath-all variable that includes levels of health, skill, education and technological knoweldge.

Under technical assumptions - (i) local non-satiation of preferences, (ii) compete markets with no frictions and no externalities, (iii) price taking behaviors, any allocation that forms a competitive equilibrium is Pareto-efficient.

However, the RBC model received several critiques:

• there's no broad evidence that strong technology shocs always affect the economy
• there's no adeguate explanation of lasting recessions
• in typical RBC models, employment fluctuactions comesfrom the household'ìs intertemporal substitution of labor, empirical studies, in reality, show little evidence about that.
• RBC models do not consider monetary shocks, but only technology shocks.
• the assumption of a unique representative agent is not accurate, small heterogenity in utilities can have a strong influence on the model.

Early Monetarism started around 1920 when Irving Fisher applied the quantity theory of money as a tool for quantitative analysis of prices, inflation and interest rates. The key concept behind is that the amount of money circulating in an economy is the primary driver of its health, inflation, and growth.

The quantity equation is the central and formal definition of this model:

• $M$: stock of money
• $V$: velocity of money
• $P$: price level
• $Y$: real GDP

The Quantity Theory (coming from the Early Monetarism) is an interpretation of the previous equation that assumes that $V$ is costant: if people’s spending habits don't change, then any change in $M$ (Money) must lead to a proportional change in $P$ In its extreme form, it predicts the neutrality of money: an exogenous increase of the stock of money is followed by a proportional increase of the price level, without any effect on real variables like consumption, output and investment.

Recall that, the velocity of money is defined as:

In the 50ies, Milton Friedman and Anna Schwartz argued that money might be neutral in the long run, but it has real effects in the short run.
They linked the previous crisis with their theories: before Friedman, most people thought the Great Depression was a failure of capitalism. Friedman and Schwartz proposed that it was actually a failure of the Federal Reserve because Fed didn't put money back into the system in moments of need, resulting in a strong credit crunch and deflation.

If compared with Keynesians, Monetarists show a different approach:

Friedman was also skeptical about discretionary policy, he proposed:

• constant-money growth rule: central banks should increase annually 3% the amount of money supplied
• avoid interest rate targeting and too low (below the natural level)
• distrust of fiscal policy: governemtn spending "crowds out" (reduce) investment and has little impact in the long run.

However, in 1980, monetarism lost his appeal for different reasons:

• the assumption on $V$ was not realistic
• it was hard to understand the definition of money stock (cash, liquid investments, cash equivalents...?)
• money growth was not a good indicator of demand

• M1 (Narrow Money): includes currency, i.e. banknotes, coins and balances that can be immediately converted into currency or used for payments.
• M2 (Intermediate Money): includes M1 + deposits with maturity up to 2 years and deposits redeemable with notice peiriod up to 3 months.
• M3 (Broad money) inclues M2 + marketable instruments issued by Monetary Financial Institutions.

Today's money architecture is structured as follows:

• Money in the hand of the public
  • cash (issued by central banks)
  • bank deposits (created by commercial banks)
• Digital central bank money: reserves created by central banks that can be only used by commercial banks to settle interbank claims.

The model, based on Lucas (1972) and Phelps (1970), starts from the following assumptions:

• the economy is populated by a laege number of farmers indexed by $i$
• each farmer produces a specific good
• each farmer selles its good in a competitive market at individual price $P_i$ and market price $P$
• revenues allow each farmer to consume a bundle of goods
• there are two 2 possible shocks:
  • prefrerence shock
  • monetary shock

For simplicity, we also add the assumption that there's perfect information. We then model each farmer's production as:

where $Y_i$ is the output and $N_i$ his amount of labour.

The budget constraint for each individual with consumption $C_i$ is:

The utility function of each individual is then:

Since there's perfect information, each individual knows the aggregate price level $P$ and can solve the optimization problem:

that leads to:

if we consider $n_i=\ln N_i$ and $y_i=\ln Y_i$, we can rewrite the first-order condition as:

Intuition: a farmer increases his production whenever the relative price of his product increases.

If we then assume that the demand function depends on the good's relative price , on real income and on a real preference shock $z_i$, we can write the log-demand as:

where $\eta$ is the elasticity of demand between goods.

Therefore, the aggregate output is given by $y={\int }_0^1{y}_i{d}_i$ and the aggregate price level by $p={\int }_0^1{p}_i{d}_i$.
(Note that the preference shock is assumed to have zero mean: ${\int }_0^1{z}_i{d}_i=0$)

We then consider aggregate demand, given by: $M=PY$ _(intuition: similar to the quantity equation with $V=1$).
In log-terms, this rewrites as:

with $m$ assumed to be stochastic $m\sim N(0,{\sigma }^2)$, representing the monetary shock (central bank's policy is unpredictable, creating random fluctuations in demand).

In equilibrium, the market has to clear, i.g. $y_i=y_i^d$:

solving for $p_i$ yields to:

if we then take the integral over all goods, we get:

Hence, we obtain the equilibrium as: $y=0$ _(remember that $y=\ln Y\to Y=1$)_and $m=p$.
For the indidual good, this means:

Intution:

• money is neutral and can only affect the price level, output is fixed at the full employment rate $Y=1$. (Classical dichotomy: monetary policy cuase nominal prices and wages to change, leaving the real equilibrium unchanged).
• the equilibrium $y_i$ depends only on the relative price $p_i$ which depends on $z_i$.

We now consider the same model with imperfect information, so each farmer only observes the price $p_i$ of his produced good but not the market price/price index $p$.

In this way, a monetary shock has real effects on output, raising aggregate demand. As the unpredicted increase of money supply generates price movements, individuals $i$ may misinterpret this partially as an increase of relative price index of a good.

In this model, output is given by the Lucas Supply Function:

Intuition:

• deviation of $y$ from its natural level is an increasing function of the surprise in the price level
• if we make use of the aggregate demand function $y=m-p$, we can solve Lucas Supply Function for $p$ and $y$:

This model argues that there's a statistical output-inflation relation: however, if policy markers attempt to take advantage of this (raising output by raising the money growth rate above the trend level), they may cause this relationsbip to break down.

However, models based on Neoclassical economy (like Lucas Supply function) are appropriate to study:

• if monetary policy has large effect if it surprises the public
• if trying to create repeatedly surprises will be futile

The main assumption behind is that prices are not completely flexible (Some models also consider wage rigidities).

Firm's profit maximization yields to the following New Keynesian Phillips Curve:

where ${\pi }_t$ represents the inflation, $y_t$ the output, $\kappa >0$ and $0<\beta <1$.

• an increasing output level leads to higher inflation
• high expected inflation tomorrow yields to higher inflation today. (If firms expect higher prices, they set higher prices today).

On the other hand, households's intertemporal consumption optimization probel yields to the following IS-cuve:

The IS-curve states that output $y_t$ depends negatively on the real interest rate and positively on the expected future output.
Also, if the real interest rate is expected to rise in the future, savings become more attractive and consumption declines.

A forward iteration of the IS-curve and the Philipps curve brings to:

Intuition: firms set their nominal prices based on the expectations of future output:

• output depends on all expected future real interest rates
• infation depends on all expected output levels.

For the analysis of the optimal monetary policy, we also add supply shocks ${\xi }_t$ and demand shocks ${\sigma }_t$, both described by an AR(1) process.

with ${\rho }_1,{\rho }_2\in (0,1)$ measure the persistence of the shocks.

The forward iteration of the IS-curve and the Phillips curve with shocks leads to:

Since output depends now also on expected future demand shocks, shocks on the IS-curve can be completely accomodated. Indeed, at the optimum, the policy maker ajusts the interest rate such that the shocks are offset.
On the other hand, cost-push shocks ${\xi }_t$ (supply shocks) generate a trade-off between output and inflation ($\to$ efficient frontier).

Criticism:

• there's no delay in the response of inflatio to shocks
• inflation is just forward-looking, past inflantion is irrilevant
• in the cases of demand shocks, disinflation can be achieved costlessly and may even generate a boom if anticipated. However, disinflations have historically entailed signficant output losses.

4. Consumption and Investment

5. The Solow Growth Model

6. Money holding: Inflation and Monetary Policy

7. Crises in Market Economies

8. IS-LM Model and Open Economy

9. Theories of exchange rate determination

10. Technical Appendix