Interpreting the Business Cycle
Business Cycles
• Real per capita GDP does not evolve in a “smooth” manner over time
— typically fluctuates around “trend”
— sometimes, “trend” appears to shift as well
• Fluctuations in GDP around “trend” are called business cycles
• No one really knows for sure why this happens
• Naturally, there are many competing theories
Schumpterian View
• The process of productivity growth is naturally a random process (a source
of shocks)
• Technological innovation is a process of “creative destruction”
— innovations typically favor some sectors over others
— even in favored sectors, innovations are slow to diffuse (so productivity
gains are in the future)
— GDP may decline in the short-run, as economy adjusts (e.g., retraining,
reallocation, etc.) to exploit future productivity gains
• Moreover, not all innovations turn out as planned
— expectations over future productivity will evolve randomly as information is updated (information shocks)
— actual productivity may be higher or lower than expected (a positive
or negative productivity shock)
— in any case, expectations are endogenous; they react “rationally” to
exogenous information events
Keynesian View
• The process of productivity growth is naturally a relatively smooth process
(not a major source of shocks)
• Shocks stem from psychological sources that alter expectations: animal
spirits (consumer confidence, business sentiment, etc.)
— expectations are exogenous; they are proactive, rather than reactive
• Expectation shocks may be either “rational” or “irrational”
— rational: an exogenous change in expectations that changes the underlying fundamentals (self-fulfilling prophesies)
— irrational: an exogenous change in expectations that bears no relation
to (and so inconsistent with) underlying fundamentals
• In any case, animal spirits are viewed as influencing economic activity
through changes in “aggregate demand”
Model 1: A Basic Schumpeterian Model
• A representative agent with preferences  ( )
• An aggregate production function  = ; where  denotes output, 
employment, and  is an exogenous productivity parameter (equal to the
real wage, in a competitive economy); Time constraint is  +  = 1
• Assume that  fluctuates randomly over time (say, around some trend);
let  ∈ {  } with   
• Solution satisfies  (∗ 1 − ∗) = 
• Assume that SE dominates WE, so that ∗() is increasing in 
Implications
• Output and employment varies over time; Employment and productivity
is procylical (tends to move in the same direction as output); Broadly
consistent with data
• Allocation is efficient: no role for government policy
• Reason: although welfare declines during a recession, economy reacts to
exogenous decline in  in the best manner possible
• In fact, government stabilization policies are generally welfare-reducing
Model 2: Animal Spirits
• A representative agent with preferences  ( )
• An aggregate production function given by  = (n) where n is aggregate employment and  is individual employment
• Assume that (n) is increasing in n (an individual expects a higher return
to their own labor , if everyone else is working harder); e.g.
=
(
  if n ≥ 
 if n  
where  is a parameter (if aggregate employment is below  individual
productivity is low; and vice-versa)
• Choice problem is now more complicated because individuals must try to
forecast n
• Conditional on some forecast n their choice problem is
max  ((n) 1 − )

• An individual’s optimal choice of  now depends on their forecast of n;
write this solution ∗(n)
• Individual solution satisfies
 ((n)∗ 1 − ∗) = (n)
• Of course, as everyone is identical in this economy, in equilibrium it must
be the case that ∗(n) = n
• And so we have one equation and one unknown determined by
((n)n 1 − n) = (n)
• Interesting fact: there can be more than one solution to this equation
— there may exist multiple equilibria
— which equilibrium occurs is determined entirely by initial expectations
of n (when people are formulating their choice problems)
— these initial expectations are not determined by economic fundamentals; they are determined by psychology (animal spirits)
• Imagine, for example, that individuals are (for some unexplained reason)
“optimistic”
— i.e., they expect n  ; so they expect  = 
— then solution is ( n  1 − n ) = 
• Imagine, instead, that individuals are (for some unexplained reason) “pessimistic”
— i.e., they expect n  ; so they expect  = 
— then solution is (n 1 − n) = 
• Now imagine that expectations fluctuate randomly (waves of optimism and
pessimism)
Implications
• Output and employment varies over time; Employment and productivity
is procylical (tends to move in the same direction as output); Broadly
consistent with data
• Allocation is inefficient: potential role for government policy
• Reason: although people are making individually-rational choices based on
their beliefs, and while beliefs are rational (consistent with fundamentals),
there is no good reason for beliefs to fluctuate in the first place
• Government policy that stabilizes output at high level  =  n is
desirable (if possible)
Discussion
• Two very different theories that deliver very similar (in fact, identical)
predictions
• Predictions are broadly consistent with observation; how can we discriminate between the two?
• An important question because (unfortunately, or interestingly) the two
theories deliver very different policy implications
• One way is to try to evaluate consequences of historical policy interventions
• But because reality is complicated, it is difficult to isolate effects in the
data (many other things are changing at the same time)
• In the meantime, people choose the theory that does least violence to their
preconceived notions; e.g.,
Model 3: Uncertainty and Rational Expectations
• Same as Model 1, except...
• let ( | ) denote probability of  conditional on information (news)
 ∈ { } and assume
( | )  ( | )
( | )  ( | )
• i.e., good news means that  is more likely and bad news means  is
more likely
• assume that people know the probability structure ( | )
— i.e., they will form “rational” expectations based on all available information
— note: expectations will react (rationally) to exogenous news events
• Timing is as follows
— news arrives (good or bad)
— individuals make employment decisions based on this news (and their
expectations of future productivity)
— productivity is then realized (high or low)
— output (and consumption) is determined by past employment decision
and current productivity
• Choice problem (conditional on news ) is
max ( | ) ( 1 − ) + ( | ) (  1 − )

• Solution is ∗()
• If  is linear in  then solution is characterized by
where
( ())∗ 1 − ∗) =  ()
 () = ( | ) + ( | )
which is expected productivity conditional on news 
• Note:  ()   (); so ∗()  ∗()
Implications
• Good news means high expected return to labor; employment boom (and
vice-versa when news is bad)
• Let  () = ()∗() denote expected output; so good news means
that expected output is high; i.e.,  ()   ()
• But actual output may turn out to be high or low, depending on realization
of  ∈ {  }
• Let  ∗( ) = ∗() denote actual output; then
 ∗( )   ()   ∗(  )
 ∗( )   ()   ∗(  )
• Output and employment fluctuate in manner consistent with observation
• It appears that “mistakes” are made; e.g.
— employment boom based on “optimism” that subsequently turns out
to be wrong (productivity turns out to be low)
— employment bust based on “pessimism” that subsequently turns out
to be wrong (productivity turns out to be high)
• These “mistakes” are consistent with rational expectations (must distinguish between ex ante and ex post)
• Equilibrium is efficient; no role for government policy
Model 4: Uncertainty and Irrational Expectations
• This is probably the closest to what many policymakers have in mind
• Same as Model 3 except...
• Assume that actual productivity always remains constant; say 0
• But continue to assume that people form expectations based on ( | )
— interpret  as “animal spirits” (i.e., good spirits, bad spirits)
— these expectations are irrational; i.e., they are inconsistent with the
underlying fundamentals (a constant 0)
• People will react to “animal spirits” when they should not; employment
will boom and bust as a consequence
• But productivity always turns out to be 0; people never learn, even though
they’re always wrong
• Output and employment fluctuate in manner consistent with data
• A definite role for government stabilization policy (assuming that policymakers are somehow more rational than their constituents)
Application: Interpreting Output Gaps
• Potential GDP: a theoretical concept describing the level of GDP that
would transpire if markets worked “perfectly”
• Output Gap: the difference between actual and potential GDP
• Problem: potential GDP is not observable (assuming that it even exists)
— so people try to estimate it, usually by drawing a “trend” line through
the data
• Problem: drawing a trend line through the data does not mean that it
represents potential GDP
— even worse, interpreting the measured output gap as evidence of market
failure is highly dubious
• Note: can identify potential GDP and output gaps in both Models 3 and
4
— markets work perfectly in Model 3, but not in Model 4