Jan 10, 2006 - Pedro Amaral and Jim McGee (2000). Jonas Fischer (2003) ... Jordi Gali (1999) : decompose productivity and hours into technology and ...
Business Cycles in a Neoclassical Growth Model: How important are technology shocks as a propagation mechanism?
Suparna Chakraborty
January 10, 2006
1
Motivation
Traditional quantitative accounting techniques of business cycles use a standard growth model with exogenous TFP shocks to numerically account for ‡uctuations in macroeconomic aggregates..
Results often show that exogenous technology shocks can almost wholly account for macroeconomic ‡uctuations.
2
What is the problem?
The only possible way that external shocks can be modelled is through ‡uctuations in Total Factor Productivity, or the Solow Residual.
The procedure is restrictive in that it rules out all other possible ways in which external frictions can a¤ect the economy.
Results erroneously overemphasize the role of TFP shocks while ignoring other important channels, which by construction are eliminated.
3
My idea
If we can use a method that allows us to extend the neoclassical growth model to incorporate other possible channels through which external frictions can a¤ect the economy, - would TFP ‡uctuations alone still almost wholly account for macroaggregates? -can we identify other potentially important transmission channels of external shocks?
The method that serves our purpose is: BUSINESS CYCLE ACCOUNTING, developed in 2002 by VV Chari, Patrick Kehoe and Ellen McGrattan.
4
Idea behind BCA
Large classes of models, including models of various frictions, can be shown to be numerically equivalent to a prototype growth model where the frictions show up as time-varying wedges, which interfere with the …rst order equilibrium conditions, just like time varying taxes would do.
5
Examples of wedges
(1) A labor market friction, like unions, or minimum wage legislation, will be replicated in a growth model by "labor wedge", which at the face value looks like a time varying tax on labor income, which will lead to a ’wedge’between the marginal rate of substitution between consumption and leisure and the marginal product of labor (or wage).
(2) An investment market friction, like "credit crunch" will be replicated as an "investment wedge", which at the face value looks like a time varying tax on investment income, which will lead to a ’wedge’ between the intertemporal marginal rate of substitution and marginal product of capital.
6
6.1
Literature review
Views favoring the traditional technique:
Pioneering study: Finn E. Kydland and Edward C. Prescott (1982) and Prescott (1986): quantitative studies of business cycles, modeling the economy like a neoclassical growth model with exogenous technology shocks (henceforth referred to as KP approach) Others who used this technique: Timothy Kehoe and Ed Prescott (2000), Fumio Hayashi and Ed Prescott (2003), Pedro Amaral and Jim McGee (2000) Jonas Fischer (2003) introduces the concept of investmentspeci…c technology shocks in the standard RBC model and shows that this type of technology shock can account for almost half of total ‡uctuations of hours worked in US.
6.2
Views contradicting the traditional technique:
Susanto Basu and John Fernald (1997) argues “calibrating dynamic general equilibrium models as if Solow residuals were technology shocks confuses impulses and propagation mechanisms” Jordi Gali (1999) : decompose productivity and hours into technology and non-technology components using VAR. He then shows that in an RBC model, responses of the economy to technology shocks are not very accurate to those observed in post war US data, non-technology shocks fare much better Peter N. Ireland (2004) looks at technology shocks in the context of New Keynesian models and agrees with Gali that other shocks, namely preference shocks, monetary shocks etc. are more important than technology shocks in explaining US post war data
7
The procedure
BCA procedure uses a standard growth model with four stochastic variables or wedges: e¢ ciency wedge At , which appears like time varying productivity; the labor wedge nt , which acts like a time varying tax on labor income, and the investment wedge xt , which acts like a tax on investment expenditure. Further, per capita government expenditure gt , is also considered as ‘government wedge’, which can have a signi…cant impact on the economy. Insert wedges one-by-one into the model and in various combinations to check to what extent can the wedges explain ‡uctuations in aggregates.
8
The economy
I assume that the economy every period comprises of a measure Nt of identical and in…nitely lived agents who are endowed with one unit of time that can be used for work and leisure.
For purposes of analysis, I assume that population grows at a constant rate every period, where the population growth rate is exogenous to the model.
I assume that there is one output that is produced and consumed in the economy.
Government balances the budget every period.
8.1
Representative Consumer’s problem:
M ax E0
1 X
t u( c ; 1 t
lt )
t=0
subject to: ct + (1 + xt)xt kt+1
wtlt(1
(1
nt) + rtkt
+ T rt
) k t + xt
nonnegativity constraints
8.2
Representative Firm’s problem
M ax yt
w t lt
r t kt
subject to: yt
F ( k t ; At l t )
8.3
Equilibrium
The equilibrium in this economy is given by a vector of price functions fwt; rtg1 t=0 and a vector of allocation functions fct; lt xt; ytg1 t=0 such that the price and allocation functions satisfy the following equations every period:
ct + xt + gt = yt (1) y t = F ( k t ; At l t ) (2) unt(ct; lt) = (1 (3) nt)Flt(kt; Atlt) uct(ct; lt) Etuct+1(ct+1; lt+1)fFkt+1(kt+1; At+1lt+1)+ (1 )(1 + xt+1)g = (1 + xt)uct(ct; lt) (4)
9
Application to Japan
9.1
Step 1: Functional forms
Preferences and technology used:
(ct (1 lt)1
u( c t ; l t ) = = log ct + (1
)
1
; when 6= 1 (5) ) log (1 lt) when =1
1
yt = kt (Atlt)1
(6)
Equations detrended by long term growth rate and substituting for consumption:
b ;A b l) ybt = F (k (7) t t t bt; g bt); lt) unt(cbt(ybt; x b b = (1 nt)Flt(kt; Atlt) (8) bt; g bt); lt) uct(cbt(ybt; x b t+1; g bt+1); lt) Etuct+1(cbt+1(ybt+1; x b b fFkt+1(k )(1 + xt+1)g t+1 ; At+1 lt+1 ) + (1 bt; g bt); lt)(1 + gz ) = (1 + xt)uct(cbt(ybt; x (9)
9.2
Step 2: Calibration procedure
I choose capital share = .36; discount factor = .972; depreciation rate = .089 and time allocation parameter 1 = 1:13 (the parameters are from Prescott and Hayashi (2002)). The time endowment is taken as 5000 hours annually, similar to Chari et. al (2005). I further assume that long-term growth rate of the per capita output is 2.15%, the average over the period 1960 to 2000. This gives the value of (1 + gz ) which is 2.15%.
9.3
Calculating the wedges:
The government consumption is taken directly from the national income accounts. I calculate the capital stock series using the initial capital stock and by the perpetual inventory method. Let us denote the vector of log deviations of the wedges o n ~ from the steady state values as est = At; e nt e xt; get , where set follows a vector autoregressive AR1 process, such that: est+1 = P0 + Pset + Q t+1
Let us denote the log deviation of any data variable ztdat from its steady state value z as z~tdat, where, z~tdat = log(ztdat) log(z ).
Now given the state of theneconomy at timeot as summa~t, we ~t; e nt e xt; get and k rized by the vector est = A can get solutions to the decision variables as function of ~t . e st and k
Since we mentioned before that this is an accounting procedure, so we know that if we insert all the wedges jointly in the model we will be able to exactly replicate the data. In other words we know that:
~t) y~tdat = y~t(est; k ~t) x ~dat ~t(est; k t =x ~ ~t) ltdat = ~ lt(est; k
(10) (11) (12)
10
Results: Decomposition
Our accounting procedure decomposes movements in variables from an initial date with an initial capital stock into four components consisting of movements driven by each of the four wedges away from their values at the initial date. We construct these components as follows.
De…ne the of the wedges by setting n e¢ ciency component o e s1t = A~t; e n0 e x0; ge0 where es1t is the vector of log deviation of wedges in period t, where the e¢ ciency wedge takes on its period t value while the other wedges stay at their initial i.e. steady state value. Thus, using ~0, we can generate and the initial period capital stock k ~t+1 = k ~t+1(est; k ~t) where the capital stock series by k ~t+1(est; k ~t) is the estimated decision rule of the capital k stock next period.
n
~t; e n0 e x0; ge0 Then, using the vector of wedges , es1t = A ~t+1 and the decision rules estimated capital stock series k estimated, we could get the movements in the decision variables due to the e¢ ciency component only. Thus, we can get:
~t) y~1t = y~t(es1t; k ~t) x ~1t = x ~t(es1t; k ~ ~t) l1t = ~ lt(es1t; k
(13) (14) (15)
o
the
11
Results
E¢ ciency wedges are important for transmitting the impact of market frictions on the economy, especially during the depression era of the nineties In contrast to the assertions of Prescott and Hayashi (2002), they are de…nitely not the only channel that we need consider. In fact, investment wedges emerge as an important transmission channel, not only during the late eighties when it played a more important role than e¢ ciency wedges, but also during the nineties, when it played a signi…cant role.
12
Implication
What is the implication?
It tells us that researchers who look for primitives behind these wedges to explain the happenings in Japan should concentrate not only on productivity ‡uctuations and market frictions that directly caused technological upheavals, but also concentrate on market frictions like the ones outlined by credit-constrained models in which market frictions play a major role in causing business cycles by a¤ecting credit ‡ows.
