Credit Crunches, Deleveraging and the
Zero Lower Bound
Standard NK model
Euler equation with discount factor shock qt
Et ct+1 ct =
1
(it Et t+1 + qt )
Calvo pricing frictions:
t = Et (t+1 ) + ct
Discount factor shocks follow autoregressive process
qt =
Miscellaneous Classification Topics
Oversampling
When classes are present in very different proportions as in 2% success (1) and 98% failure (0)
and in the case that the benefits of identifying a success are much greater than the loss due to missspecifyin
Real Rigidities
NK models vs. Data
Data: long-lived eects from monetary shocks
half-life = 10 quarters
Models: half-life 1/2 - 2/3 average price durations
E.g. Calvo with = prob. of not changing prices
yt = yt1 + t
Half-life with = 1 1/12 is 8 mos.
Ne
3
Segmented Markets
Standard monetary models (cash-in-advance, money in utility function) imply, counterfactually,
that a persistent increase in the money supply increases nominal interest rates since expected
ination increases. In contrast, in the data n
7
Innovation, Technology Adoption and Firm Dynamics
7.1
Parente (JET, 1994)
Studies economy in which rms choose the timing of a technology adoption. Adopting a better
technology entails a) a xed cost and b) loss of expertise. There is also learning-by-doi
4
Misallocation
We study models in which wedges in the rms Euler equations for hiring capital/labor generate aggregate TFP losses. We study two mechanisms that generate such wedges: i) heterogeneity in markups across producers and ii) nance frictions. We
1
Economies with Fixed Price Adjustment Costs
A widely held view in macroeconomics is that changes in monetary policy (or more broadly
nominal, nancial and demand shocks) have eects on real activity because prices are sticky.
Price stickiness is usually m
1
Firm Dynamics
We next extend the tools we have learned to an environment in which heterogeneity is on
the rm side. In particular, we extend the equilibrium concept we used above to allow
for rm entry and exit. The model we study below is a variant of th
TIME SERIES REGRESSION NOTES
Time series regression analysis is tricky! Be careful and dont generate spurious results.
1. Transform all variables (both dependent variable and explanatory variables) to
stationary form. Then your equation will be balanced.
1
A Dynamic Production Economy
The economy lasts for two periods and is populated by households, rms and by the
government. All markets are assumed to be competitive, so both households and rms
take prices as given. The government taxes labor income at ra
1
Facts on the US historical growth experience, aka
the Kaldor facts
In 1958 Nicholas Kaldor listed 4 key facts on the long-run growth experience of the US
economy in the past century, which have revealed to be still true today and true, to a
large extent
1
Optimal Taxation of Labor Income
Until now, we have assumed that government policy is exogenously given, so the government had a very passive role. Its only concern was balancing the intertemporal
budget. In this section, we let the government be more p
1
Endogenous Growth
We present two models that are very popular in the, so-called, new growth theory
literature. They represent economies where, notwithstanding the absence of exogenous
technical progress, output per capita grows permanently.
1.1
AK Model
1
Eciency Wages and Unemployment
The idea of the eciency wage model is that how much the worker is paid aects
his performance on the job. As a result, a rm may be willing to pay a higher wage
than the one that is determined competitively because this ind
1
Asset Pricing: Bonds vs Stocks
The historical data on nancial asset returns show that one dollar invested in the DowJones yields 6 times more than one dollar invested in U.S. Treasury bonds. The return
on stocks is roughly 6% in real terms (i.e., after
1
The Economy
In every economic model it is useful to specify in detail the following features of the
economy:
Time: whether the economy is static (one-period), or dynamic (two or multiple
periods)
Agents: households, rms and government.
Commodity set:
1
Competitive Equilibrium
Each household and each rm in the economy act independently from each other,
seeking their own interest, and taking as given the fact that other agents will also seek
their best. In the previous section we have described the beha
1
Intertemporal Choices
We now extend our framework to incorporate intertemporal decisions, i.e. decisions
that involve a trade-o between the present and the future. The vast majority of
important economic decisions are of this type:
the consumption deci
1
Investment Theory
We now consider the problem of an innitely lived rm that in every period chooses
how much to invest, i.e., how much to add to its stock of productive capital. Note the
dierence with the way we modelled the rm so far: we are used to thi
1
Equilibrium Unemployment
The idea of modelling labor markets as frictional markets (i.e., markets which do
not clear) is due to Diamond, Mortensen and Pissarides. For this idea, they won
the Nobel Prize in Economics in 2011. The specic version of the m
1
Unemployment: Facts and Models
1.1
Facts
Denote the population of working age 16-65 at time as This segment of the population can be divided into 3 groups. First, the group of all the individuals who hold a
job at time , called employment, denoted by Se
1
Consumption and saving under uncertainty
1.1
Modelling uncertainty
As in the deterministic case, we keep assuming that agents live for two periods. The
novelty here is that their earnings in the second period are uncertain. Uncertainty is
dened in terms
1
Risk Aversion
We introduce here the notion of risk aversion, which is key in economies with uncertainty.
Consider an individual with consumption who faces a bet that pays a random amount
with () = 0 and () = What is the premium that the individual woul
1
Social Security
In the U.S. economy, and in the majority of developed countries, there is a Pay-As-YouGo (PAYG) social security system in place: all young workers alive in a given period pay
into a general fund administered by the Government (Trust Fund
1
The Permanent Income Hypothesis
1.1
A two-period model
Consider a two-period model where households choose consumption (1 2 ) to solve
max log 1 + log 2
cfw_1 2
2
1 +
1+
=
1+
1
1+
+
where is the discount factor, the interest rate. The term is the per
1
Ricardian Neutrality of Fiscal Policy
We start our analysis of scal policy by stating a neutrality result for scal policy
which is due to David Ricardo (1817), and whose formal illustration is due to Robert
Barro (1974). The Ricardian proposition can be