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FINANCIAL CRISES AND
TOTAL FACTOR PRODUCTIVITY
Felipe Meza
Erwan Quintin

Center for Latin American Economics
Working Paper 0105
Center for Latin American Economics
Working Paper 0201
March 2005

FEDERAL RESERVE BANK OF DALLAS

Financial Crises and Total Factor Productivity
Felipe Meza

Erwan Quintin

Universidad Carlos III de Madrid

Federal Reserve Bank of Dallas∗

March 22, 2005

Abstract
Total factor productivity (TFP) falls markedly during ﬁnancial crises, as we document with recent evidence from Mexico and Asia. These falls are unusual in magnitude and present a diﬃcult challenge for the standard small open economy neoclassical
model. We show in the case of Mexico’s 1994-95 crisis that the model predicts that
inputs and output should have fallen much more than they did. Using models with
endogenous factor utilization, we ﬁnd that capital utilization and labor hoarding can
account for a large fraction of the TFP fall during the crisis. However, these models
also predict that output should fall signiﬁcantly more than in the data. Given the behavior of TFP, the biggest challenge may not be explaining why output falls so much
following ﬁnancial crises, but rather why it falls so little.

Keywords: Financial crises; total factor productivity; output ﬂuctuations
JEL classiﬁcation: E32; F41; J24

∗

Corresponding author. Felipe Meza: Universidad Carlos III de Madrid, Calle Madrid 126, Getafe,
Madrid 28903, Spain, +34 91 624 57 34 (phone), +34 91 624 98 75 (fax), fmeza@eco.uc3m.es. Erwan
Quintin: Research Department, Federal Reserve Bank of Dallas, 2200 N. Pearl St. Dallas, TX 75201,
+1 214 922 51 57 (phone), erwan.quintin@dal.frb.org. Felipe Meza thanks the Ministerio de Educación y
Ciencia de España for ﬁnancial support through project SEJ2004-00968. We thank seminar participants
at the European Central Bank, Rice University, the University of Texas at Austin, ES European Meeting
Madrid 2004, ASSET Meeting Barcelona 2004 and the Banco de México for their comments. The views
expressed herein are those of the authors and may not reﬂect the views of the Federal Reserve Bank of
Dallas or the Federal Reserve System.

Introduction

Output falls drastically following ﬁnancial crises, much more than what the behavior of
capital and labor would lead one to expect. In the language of growth accounting, total
factor productivity (TFP) falls markedly during ﬁnancial crises, as we document with recent
evidence from Mexico and East Asia. The magnitude of these falls is unusual: TFP falls
by more than two standard deviations in all the cases we study. These declines are also
puzzling because given their size, a standard small open economy model would predict that
hours worked, capital and output should fall much more than they do in the data. Our goal
in this paper is twofold: document the unusual behavior of TFP during crises, and describe
the challenge that this behavior poses for standard small open economy neoclassical models.
Most of the existing literature focuses on what triggers a ﬁnancial crisis in the ﬁrst
place. For instance, in the case of Mexico’s 1994-95 “Tequila” crisis, Flood, Garber, and
Kramer (1996) and Calvo and Mendoza (1996) study the role played by ﬂow imbalances
(liquid ﬁnancial assets vs. broad monetary aggregates, and short-run debt vs. gross foreign
reserves). Cole and Kehoe (1996) and Sachs, Tornell and Velasco (1996) conjecture that
Mexico’s large stock of short-term debt may have given rise to a self-fulﬁlling debt crisis.
These and many related articles have shed light on what causes ﬁnancial collapses in nations
like Mexico, but they do not try to account for the behavior of output after the collapse.
Like Calvo (2000) and despite some exceptions which we review below, our assessment is
that there has been little emphasis on the deep consequences of crises on real activity. This
paper contributes to ﬁlling this gap.
We study the real impact of ﬁnancial crises in the context of various versions of the
standard small open economy neoclassical model (as articulated for instance by Mendoza,
1991) and concentrate our attention on Mexico’s Tequila crisis. While ﬁnancial crises share
many characteristics, a satisfactory quantitative study of the real impact of these episodes
must incorporate country-speciﬁc features. In the case of Mexico’s Tequila episode, a number
of deep policy shocks accompanied the crisis. In particular, the Mexican government sharply
raised energy prices and the Value Added Tax (VAT) rate in the ﬁrst quarter of 1995. We
model those shocks explicitly and ﬁnd that changes in consumption taxes and the price of
1

energy in 1995 had an important eﬀect on output. However, the impact of these ﬁscal shocks
is markedly smaller than the impact of TFP. Our key result is that given the size of the fall
in TFP Mexico experienced in 1995, hours worked, capital and output should have fallen
twice as much as they did, in percentage terms.
The fact that the behavior of factor series diverges so much from the predictions of
the standard model suggests that factor hoarding plays a large role during ﬁnancial crises.
Intuitively, one should expect large swings in capital utilization and eﬀort during crises. For
several quarters, interest rates are well above average, while TFP is well below average. This
gives ﬁrms strong incentives to postpone the consumption of capital services (say, by leaving
plants or machines temporarily idle) and economize on variable expenditures such as wear
and tear until conditions improve. Similarly, if employment is costly to adjust, ﬁrms may use
the eﬀort margin to respond to the fall in the marginal product of labor. Standard models
of factor hoarding (Greenwood, Hercowitz and Huﬀman, 1988, and Burnside, Eichenbaum
and Rebelo, 1993) suggest that capital utilization and labor hoarding can account for a
large fraction of the variance of TFP both during and outside the crisis period in Mexico.
Nevertheless, we also ﬁnd that modeling factor hoarding explicitly may not resolve the output
puzzle. The models we consider continue to predict that, following the crisis, output should
fall much more than in the data.
Our calculations complement some related investigations of the real impact of ﬁnancial
crises by stressing the importance of TFP. Most existing studies ignore the unusual behavior
of TFP.1 Among the few exceptions, Burstein, Eichenbaum and Rebelo (2002) study the
behavior of inﬂation and output in Mexico and South Korea in a model with credit market
frictions and four sectors: local, export, tradable and non-tradable goods. The model pro1

Burnside, Eichenbaum and Rebelo (2001), Corsetti, Pesenti and Roubini (1999) and Lahiri and Vegh
(2002) provide qualitative explanations for the contraction of output. Cavallo, Kisselev, Perri and Roubini
(2004) show that large falls in output are possible after crises in sticky-price models with a margin constraint.
Similarly, Cook and Devereux (2005) simulate recent crises in Malaysia, South Korea and Thailand and show
that output can drop sharply following shocks to a country’s risk premium. All these papers assume that
TFP is constant. Mendoza (2002) shows that a ﬂexible-price model with a liquidity constraint can lead to
sudden stops of capital ﬂows and large output falls. He allows for TFP ﬂuctuations, but only of average
business cycle size: the standard deviation of TFP ﬂuctuations coincides with that of output. Chari, Kehoe
and McGrattan (2005) show that sudden stops of capital ﬂows induce an output increase, not a fall, in a
standard neoclassical model. They argue that more research is needed to ﬁnd a “friction” that can overwhelm
the positive eﬀect of a sudden stop. Our results suggest that explicitly modeling and measuring TFP should
suﬃce.

duces a yearly fall in output that slightly exceeds the actual fall in Mexico in 1995 provided
TFP falls by 50% in the export sector. They do not provide any evidence that such a fall
took place in 1995. Gertler, Gilchrist and Natalucci (2003) simulate the impact of shocks to
a country’s risk premium in a model with price-stickiness and endogenous capital utilization.
Their model can predict a fall in output in South Korea of a magnitude similar to the one
observed. They argue that measured TFP varies because capital utilization does. However,
their quantitative analysis does not rely on measures of TFP that are consistent with the
model: adjusted TFP remains constant during experiments. Our calculations suggest that
in the Mexican case, capital utilization accounts for less than 30% of the fall in TFP. Similar
calculations could be carried out for Asian nations.2
Given our ﬁndings, quantitative studies of the real impact of ﬁnancial crises should take
the behavior of TFP into account. Given the precipitous fall in TFP that follows crises
episodes, the most puzzling aspect of ﬁnancial crises may not be that output falls a lot, but
rather that it falls too little.

Evidence

In this section we document the fact that ﬁnancial crises are followed by unusually large
falls in TFP and GDP using evidence from Mexico’s 1994 crisis, and from the 1997 crisis in
South Korea and Thailand. In addition, we ﬁnd that these falls are persistent. Both GDP
per capita and TFP remain below trend for several years after the crisis.
To measure TFP, we use the following speciﬁcation of aggregate technological opportunities:
,
Yt = At Ktα L1−α
t
where Yt denotes GDP at date t, Kt is aggregate capital, Lt denotes aggregate hours worked
and α ∈ (0, 1) measures the importance of capital in production. We assume that At ,
2

With the data we present in the next section and using the capital utilization model of Greenwood,
Hercowitz and Huﬀman (1988), one can calculate the fall in TFP adjusted for capital utilization in South
Korea and Thailand in 1998. We set φ = 1.5 which, assuming long-term interest rates of 4%, implies a
steady state rate of depreciation of 8%. Given those parameters, capital utilization can account for only 36%
and 17% of the fall of measured TFP in South Korea and Thailand, respectively.

aggregate TFP at date t, equals zt (1 + γ)t(1−α) , where zt is stationary and γ ≥ 0 is an
exogenous growth rate. Let yt , kt and lt denote the per capita counterparts of Yt , Kt and
Lt , respectively. In the neoclassical growth model, per capita output and capital grow at
constant rate γ along the balanced growth path, while per capita hours worked are constant.
Letting yt and
kt be detrended per capita output and capital, we have
ktα lt1−α .
yt = zt
kt and lt . We construct capital stock series
Measuring zt requires empirical counterparts for yt ,
using the perpetual inventory approach with geometric depreciation and yearly data from
the International Financial Statistics (IFS) database (IMF, 2004). The IFS database reports
nominal data on investment. Like Bergoeing, Kehoe, Kehoe and Soto (2002) we measure real
investment as the ratio of nominal gross ﬁxed capital formation to nominal GDP multiplied
by real GDP. We assume that capital depreciates at a yearly depreciation rate of 8%. To
set the initial capital stock, we follow Young (1995) and assume that the growth rate of
investment in the ﬁrst ﬁve years of the series is representative of the growth of investment in
previous years. The resulting capital stock series begins in 1963 for Mexico and Thailand,
and 1966 for South Korea. GDP series start in 1950 for Mexico and Thailand, and in 1953
for South Korea. For Mexico, we use total hours worked as measured in Bergoeing, Kehoe,
Kehoe and Soto (2002). They report the product of total employment and average hours
per worker in the manufacturing sector, as measured with data from a manufacturing sector
survey. Calculations are similar for South Korea and Thailand except that an estimate of
average hours worked is available for most sectors in those two countries.3 Labor series cover
the periods 1980-2000, 1970-2002 and 1989-1999 for Mexico, South Korea and Thailand,
respectively.
3

For South Korea, we use data on total employment and average hours worked per week, as reported
by the South Korean National Statistical Oﬃce. Total employment corresponds to employed individuals of
age 15 and higher in all sectors. Average hours worked correspond to all industries, excluding agricultural
activities. Data were downloaded from http://www.nso.go.kr. For Thailand, total employment corresponds
to employed individuals of age 13 and higher in all sectors, as reported by the International Labour Oﬃce
(ILO) and the Thai National Statistical Oﬃce. Average hours worked correspond to all industries, excluding agricultural activities and public administration, as reported by the ILO. Data were downloaded from
http://www.nso.go.th and http://laborsta.ilo.org.

We calculate yt , kt , and lt by dividing Yt , Kt and Lt by the number of adults between
ages 15 and 64.4 Population series for the three countries start in 1960. Detrended variables
kt are yt and kt divided by the average geometric growth factor of yt in the period
yt and
before the crisis episode. This factor is 1.7% for Mexico between 1960 and 1994, 5.3% for
South Korea between 1960 and 1997, and 4.4% for Thailand between 1960 and 1997. Finally,
we set α = 0.3. Gollin (2002) ﬁnds that after distributing the income of the self-employed to
capital and labor income, labor income shares do not vary much across countries and time,
and take values around 70%.5
Figure 1 shows the resulting series for Mexico, Thailand and South Korea with vertical
lines marking the onset of each crisis. Output falls by over 10% in all countries during the
year following the crisis, and by as much as 15.6% in Thailand. Capital, on the other hand,
remains practically constant after the crisis, and hours fall less than output in all cases. In
fact, in Mexico and Thailand, hours worked fall by less than 2%. In South Korea, hours
worked fall by a larger 8.6% in 1998. Since capital and labor fall relatively little during crises,
TFP has to fall by a large amount to account for the fall in output: 15.1% in Thailand, 7.1%
in South Korea and 8.6% in Mexico. The magnitude of these falls is very unusual for all
countries. Yearly falls in GDP and TFP exceed two standard deviations. Also notice that
the falls in output and TFP triggered by crises are quite persistent. They remain below
trend in all cases for several years. Like us, Cook and Devereux (2005) ﬁnd that output
remains persistently below trend in Asia after 1997, using a diﬀerent detrending procedure.
They report that in Malaysia, South Korea and Thailand, output remains below trend for
at least 8 quarters.
Naturally, these results could be sensitive to some of our measurement assumptions.
Young (1995) argues for instance that data on changes in inventories are of poor quality
in East Asia. Excluding changes in inventories from our calculations had negligible consequences on our results.6 Changing (1 + γ) to 1.02 for all countries, the value Kehoe and
4
We use population data for Mexico as reported by Bergoeing et al. (2002). For South Korea, data
were downloaded from http://www.nso.go.kr. For Thailand, data were obtained from the World Bank
Development Indicators database (World Bank, 2004).
5
Young (1995) ﬁnds a value of 1 − α = 0.703 for South Korea with data from the 1966-1990 time period.
6
Our TFP ﬁndings for South Korea can be compared to results in Young (1995). He reports that the
average logarithmic annual growth rate of At in South Korea was 1.7% between 1966 and 1990. The main
diﬀerence between his calculations and ours is that he takes into account changes in the quality of labor

Prescott (2002) propose,7 also has little eﬀect on results, with one minor exception. In
the case of South Korea, the eﬀect of the 1997 crisis becomes less persistent as yt and zt
surpass their 1997 levels by 2000. Next, one can carry out all calculations using national
sources of data for yt and
kt instead of IMF data.8 National Income and Product Account
series are much shorter because countries modify their systems of national accounts every
now and again, which makes results more sensitive to the choice of initial capital. On the
other hand, IMF data include only the most basic national accounts variables. Data from
national sources are richer and allow one to construct more accurate empirical counterparts
of theoretical variables, as we do in the next section. In particular, one can subtract indirect business taxes from GDP, impute the returns of government capital and of the stock
of durable goods, and include public investment and durable goods purchases in investment
(with diﬀerent rates of depreciation for each type of capital.) After making those corrections,
the behavior of detrended series changes little. It is still the case that the falls in yt and zt
after ﬁnancial crises are unusually large.9
In summary, recent ﬁnancial crises triggered unusually large falls in detrended GDP per
capita and TFP in Mexico and East Asia. There is also some evidence that these falls are
persistent. These facts beg several interesting questions. In the remainder of the paper, we
study whether given the behavior of TFP a standard small open economy neoclassical model
can account for the behavior of output and inputs in the Mexican case.
and capital. After excluding inventory changes as he does, we calculate that the average logarithmic annual
growth rate of At for South Korea for the period 1970-1990 is 2.6%. The diﬀerence is large and is due to
Young’s adjustment for quality. Assuming a labor income share of 70% and using Young’s data on raw
inputs, we ﬁnd that At in South Korea grew at an average rate of 2.7% between 1970 and 1990. In other
words, our measurement of TFP leads to the same growth rate as the one found in Young (1995) if no
adjustment for input quality is made.
7
This is the US trend. They interpret productivity as the stock of knowledge useful in production and
argue that knowledge is not country-speciﬁc.
8
Mexican data were downloaded from http://dgcnesyp.inegi.gob.mx. South Korean data were downloaded
from http://www.nso.go.kr. Thai data were downloaded from http://www.nso.go.th.
9
Carrying out these adjustments can have important consequences for some countries where ﬁnancial
crises took place. For example, Indonesian GDP per capita fell by 13.1% between 1997 and 1998. If IBT are
eliminated from GDP, then the fall in GDP is 8.0%. These adjustments make data consistent with variables
in the simplest growth model.

The small open economy neoclassical model

This section evaluates the consistency of the small open economy neoclassical model with
the behavior of output and inputs after the Mexican crisis of 1994. We model the crisis
as exogenous shocks to TFP and interest rates. Feeding these shocks into the model yields
paths for endogenous variables that we compare to data.
Because Mexico underwent deep ﬁscal changes in 1995 as part of the government’s response to the crisis, we study a benchmark model where agents face distortionary taxes on
consumption, capital income, and labor income. Also for ﬁscal reasons, Mexico’s government
signiﬁcantly raised energy prices in 1995. To control for the impact of this shock, we model
the role of energy in production. Incorporating these elements will enable us to measure the
quantitative impact of ﬁscal shocks on the behavior of output in Mexico in 1995. But this
complicates computations by preventing us from solving a standard planner’s problem.

3.1

Benchmark model

Consider an economy in which time is discrete and inﬁnite. The economy contains a continuum of mass one of identical households, and a continuum of mass one of identical ﬁrms.
Households live forever. They order consumption and labor supply sequences {ct , lt }+∞
t=0
according to the following intertemporal utility function:
+∞

t=0

ρ
β t log ct − ltν ,
ν

where β ∈ (0, 1) is the discount factor, ν > 1 determines the wage elasticity of labor supply
and ρ > 0 measures the disutility from working. With these preferences, labor supply
depends only on the current wage, wt , and is independent of consumption or income. These
preferences are commonly used in small open economy models (see e.g. Mendoza 1991,
2002, Correia, Neves and Rebelo, 1995 and Neumeyer and Perri, 2001). Correia, Neves and
Rebelo (1995) argue that they improve the ability of small open economy models to replicate
business cycle regularities.10
10

Correia et al. (1995) and Neumeyer and Perri (2001) point out that these preferences are not consistent
with a balanced growth path, unless the disutility of working increases with the rate of labor-augmenting

Households have access to an international capital market where one-period risk-free
claims to a unit of the consumption good earn exogenous return rt at the beginning of
period t. We denote by at the risk-free asset holdings of households in period t. Households
can also invest in physical capital, which they sell to ﬁrms at price 1 + rtk . Let kt be the
quantity of capital held by households in period t. Adjusting capital across periods carries
cost
ψ
(kt+1 − kt )2 ,
2
where ψ > 0. As is well-known, adjustment costs are necessary in open economy models
to prevent investment from being counterfactually volatile. Assuming that adjustment costs
are borne by households rather than ﬁrms is immaterial. An equivalent decentralization
would have ﬁrms make investment decisions and bear adjustment costs. The speciﬁcation
we use shortens the exposition by keeping the ﬁrm’s problem static.
Households also face three types of taxes. In period t, consumption is taxed at rate τtc ,
labor income is taxed at rate τtl , and returns on physical capital and international assets are
taxed at rate τtk . In addition, households receive transfer Tt from the government. Therefore,
households face the following budget constraint at date t:

ψ
ct (1 + τtc )+kt+1 +at+1 = lt wt 1 − τtl +at (1+rt 1 − τtk )+kt (1+rtk 1 − τtk )− (kt+1 − kt )2 +Tt .
2
We also assume that household borrowing is bounded below so as to rule out Ponzi schemes,
and that the bound is low enough to never bind in equilibrium.
At date t, ﬁrms transform physical capital ktf , energy et and labor nt into quantity
αk
nαt n eαt e of the consumption good, where zt is TFP. Energy is available perfectly
yt = zt ktf
elastically at price pet in date t. Fraction δ > 0 of the physical capital ﬁrms purchase from
households depreciates within each period. Therefore, at date t, ﬁrms choose (nt , ktf , et ) to
maximize:

αk

nαt n eαt e + (1 − δ)ktf − ktf 1 + rtk − nt wt − et pet .
zt ktf

technological change. In our model, there is no technological change. We follow Greenwood et al. (1988)
and compare model predictions to data which have no trend. Mexican GDP per working age person displays
no growth on average between 1980 and 2003.

The government collects tax revenues τtc ct + τtl lt wt + τtk at rt + kt rtk at date t. We assume
that tax revenues and energy sales are rebated lump-sum to households. At date t, the
government’s budget constraint is:

τtc ct + τtl lt wt + τtk at rt + kt rtk + et pet = Tt .

(3.1)

We now deﬁne an equilibrium under the simplifying assumption that agents perfectly foresee the path of TFP, taxes and the exogenous interest rate. In the quantitative section, we
consider other assumptions on expectations. Given an initial stock of capital and initial international assets (k0 , a0 ), an equilibrium in this environment is sequences of wages and prices of

+∞
capital wt , rtk t=0 , consumption, labor supply and savings sequences {ct , lt , kt+1 , at+1 }+∞
t=0 ,
sequences of labor, capital and energy demands

nt , ktf , et

+∞
t=0

, and a sequence {Tt }+∞
t=0 of

transfers such that, given prices, 1) {ct , lt , kt+1 , at+1 }+∞
t=0 solves the household’s problem, 2)
nt , ktf , et

+∞
t=0

solves the ﬁrm’s problem, 3) the market for physical capital clears (kt = ktf

for all t), 4) the labor market clears (nt = lt for all t) and 5) transfers satisfy (3.1). We
will now ask whether this benchmark model can account for the behavior of output, labor,
capital and energy after Mexico’s Tequila Crisis.

3.2

Data and calibration

Computing the predictions of this benchmark model for Mexico requires paths for exogenous shocks {zt , rt , pet , τtc , τtk , τtl }+∞
t=0 that are consistent with the theory. This requires a few
adjustments to national income and product accounts data. Date t TFP in the benchmark
model is:
zt =

yt
αk αn αe .
kt nt et

(3.2)

Therefore, we need empirical counterparts for the theoretical variables yt , kt , nt , and et .
Appendix A describes the procedure we use in some detail. Our basic approach closely follows
Atkeson and Kehoe (1999). We use quarterly data to construct the empirical counterparts of
theoretical variables. National accounts data are from Mexico’s national statistical institute
(INEGI). There are four key conceptual diﬀerences between GDP as reported in the Mexican
9

national accounts (measured GDP) and output yt in the model. First, yt equals the sum
of payments to labor, capital and energy, i.e. yt = wt nt + (rtk + δ)kt + pet et . GDP, on the
other hand, treats energy as an intermediate output and thus corresponds to yt − pet et =
wt nt +(rtk +δ)kt . Second, there is no energy-producing sector in the model, whereas measured
GDP includes the value added by the energy sector. Third, measured GDP includes indirect
business taxes (IBT), whereas output yt does not. Finally, output includes the return to all
types of capital in the model, whereas measured GDP does not. It excludes the return on
government capital and the return plus depreciation of the stock of durable goods. We make
the four corresponding adjustments to measured GDP to construct a measure of output
consistent with yt . We call this adjusted GDP measured gross output. We also construct
capital, labor and energy series that are consistent with the model. In particular, we take
into account the fact that in the model there is no energy-producing sector, and that in the
model only ﬁrms use energy.
Besides empirical counterparts for yt , kt , nt , and et , three technological parameters must
be calibrated before measuring TFP. We assume that the share of labor income in GDP is
0.7. This assumption is supported by the work of Gollin (2002), who ﬁnds that after taking
into account the income of the self-employed, labor income shares take values around 70%,
across a large set of countries, and across time. We assume that the share of labor income in
the energy-producing sector in Mexico is also 70%.11 Given these assumptions, factor shares
equal:
GDP
= 0.664,
Measured gross output
GDP
= 0.285,
= 0.3
Measured gross output
Energy expenditure
= 0.051,
=
Measured gross output

αn = 0.7
αk
αe

where all ratios are set to average yearly values. Having set those parameters, we generate
a series for TFP using equation (3.2) in each period.
Turning now to exogenous shocks other than TFP, we calculate the interest rate rt in
11

Verifying that this assumption is appropriate is diﬃcult in the case of Mexico since Mexican national
accounts do not provide compensation of employees data for oil and electricity companies.

period t as
rt =

(1 + T bill ratet ) (1 + MX Brady spreadt )
− 1,
1 + US inf lationt

where T bill ratet is the interest rate on US Treasury bills, MX Brady spreadt is the spread
between the return paid by (dollar-denominated) Mexican Brady bonds and the interest
rate paid by US Treasury bills, and US inf lationt is the relative change in the US GDP
deﬂator. In other words, our proxy for rt is the real return paid by Mexican Brady bonds.12
Our sample of Mexican Brady bond data starts in the last quarter of 1990 and ends in the
ﬁrst quarter of 2003. We measure the price of energy as a weighted average of the nominal
price of natural gas, gasoline and electricity divided by Mexico’s GDP deﬂator.13 Finally,
we calculate taxes on consumption, labor income and returns from capital and international
assets using the method of Mendoza, Razin and Tesar (1994).14 The calculated taxes are
average eﬀective tax rates, i.e the ratio of tax revenue to tax base.
Figure 2 plots the measured shocks. Most of these series underwent unusually large
changes in 1995. In particular, and not surprisingly given the fact that capital and labor fall
much less than output during 1995, TFP falls markedly during 1995. Measured gross output
fell 10.1% between the last quarter of 1994 and the last quarter of 1995, while capital fell
by 0.7%, labor fell by 2.5%, and energy fell by 24.4%. Given these data and our calculated
technological shares, TFP must fall by 7.1% to account for the fall of measured gross output
in 1995. Interest rates measured in annual terms rise from 8.7% on average during 1994
to 19.5% in the ﬁrst quarter of 1995. The price of energy jumps by 43% between the last
quarter of 1994 and the ﬁrst quarter of 1995. The consumption tax rate rises from 10.4% to
12

Neumeyer and Perri (2001) use a similar construct to study the relationship between business cycles and
international interest rates in developing countries. We use end of quarter rates, using average rates does
not alter our quantitative ﬁndings.
13
We follow the method used by Atkeson and Kehoe (1999). Appendix A provides the details. We are
constrained to use yearly data on prices and sales of energy to calculate the average price of energy. We
assume that the nominal prices of diﬀerent kinds of energy remain constant throughout each year. The
Mexican government typically adjusts energy prices either at the end or at the beginning of each year.
14
Only data on total income tax revenues are available in Mexico. We follow the estimate reported
in Fernandez and Trigueros (2001) to split total income tax revenue into its components: individual and
corporate. We use these components to measure the tax rate on labor income, and on capital and asset
returns. Also, when measuring consumption taxes using OECD data, Mendoza et al. (1994) exclude the
“Other taxes” item. Because this last item is large in magnitude in Mexico, we choose to include it. We are
constrained to use yearly data to measure taxes. We assume in the numerical experiments that taxes remain
constant throughout each year.

13.3% from the last quarter of 1994 to the ﬁrst quarter of 1995. On the other hand, the tax
rate on labor shows almost no change, falling from 12.5% to 12.2% between 1994 and 1995.
The tax rate on capital income falls from 9.5% to 7.4%.
Overall, the Mexican economy underwent a number of severe negative shocks in 1995.
We will now argue that given the magnitude of these shocks, the model predicts that output
should have fallen much more than it did. We will also argue that the quantitative impact
of changes in ﬁscal policy is small compared to the role of TFP. To make these points, we
ﬁrst need to calibrate preference and adjustment cost parameters. One way to calibrate
the model would be to assume that at a given date Mexico was on a balanced growth path.
However, we do not think that such an assumption is appropriate. Mexico underwent a series
of deep crises in the 1980s after decades of brisk growth. Between 1980 and 2003, GDP per
capita did not grow in Mexico, and we do not believe this to be a balanced growth path.
Our calibration strategy consists of choosing parameter values to match certain statistical
properties of inputs and investment before 1995.
Preference parameters ρ and ν determine the level and volatility of labor supply, respectively. We set ρ to match the average of our measure of hours worked per working age adult
before 1995. As for ν, we begin by setting it to 1.5, which implies a wage elasticity of labor
supply of 2, the value used in Mendoza (1991).15 It falls within the range mentioned by
Greenwood, Hercowitz and Huﬀman (1988), who cite studies of labor supply in the United
States. We were unable to ﬁnd similar studies for Mexico. Setting ν = 1.5 implies a volatility
of hours worked that is near its pre-crisis counterpart in Mexico. The next section provides
some sensitivity analysis on this key parameter. In this benchmark model the predicted path
for input and output series is independent of β. We simply set it as in Correia, Neves and

Rebelo (1995) to satisfy β 1 + r 1 − τ k = 1, where r and τ k are the long run values of
the international interest rate and the tax on the return on international assets. This assumption is necessary for an equilibrium with zero long run growth of consumption to exist.
To obtain a long run value for the interest rate, we assume that the value it takes in the
ﬁrst quarter of 2003 (0.9% at a quarterly rate), the last date in our sample, will be Mexico’s
cost of international funds in the future. We also use the last value for τtk in our sample
15

The elasticity of labor supply is

1
ν−1 .

(9.1%) as the long run value of the tax on capital income. Next, we choose ψ, the capital
adjustment cost parameter, to match the observed standard deviation of the investment to
measured gross output ratio before 1995. The resulting aggregate adjustment costs amount
to a negligible fraction of GDP. Finally, in all quantitative experiments, we scale the relative
price of energy to match the average energy level prior to 1995.
Having set all parameters, we calculate the path our model predicts for inputs and output
under two assumptions on agents’ expectations. In the ﬁrst experiment (perfect foresight,
PF) we assume that agents know the entire sequence of exogenous shocks shown in Figure 2
before making any decision. In the second experiment (perfect surprise, PS) we assume that
agents foresee all shocks up to the last quarter of 1994. After 1994, agents expect all shocks
other than the interest rate to permanently assume their average values before 1995. As for
the interest rate, households expect it to be constant at

β −1 −1
,
k
1−τaverage

the only value compatible

k
is the average capital income tax rate
with zero long-run consumption growth, where τaverage

before the crisis. In other words, under the PS scenario, agents do not expect a crisis to
occur in 1995. When they observe the values of shocks in the ﬁrst quarter of 1995, agents
immediately revise their expectations of future shocks to the correct path. We view this
experiment as an approximation to a situation where households assign a positive but very
small probability to the possibility of a crisis in 1995. These simplifying assumptions on
expectations enable us to use a simple non-linear solution method based on Euler equations.
Speciﬁcally, ﬁrst order conditions from the ﬁrm and the household problems’ imply that
the evolution of capital in this model is described by the following second-order diﬀerence
equation for all t:

k
)=
1 + rt+1 (1 − τt+1

k
1 + αk kyt+1
−
δ
1 − τt+1
+ ψ (kt+2 − kt+1 )
t+1
1 + ψ (kt+1 − kt )

(3.3)

Given the initial level of capital, we use a shooting algorithm to ﬁnd the path of capital such
that endogenous variables converge to steady state when exogenous variables stay at their
level in the ﬁrst quarter of 2003 forever. Appendix B provides details. The equilibrium path
for other endogenous variables can then be calculated as a function of capital and exogenous
shocks. Given the magnitude of shocks in 1995, using linear approximations around the
13

steady state would yield inaccurate results.16

3.3

Results

Figure 3 plots the predictions of the model for GDP, labor, the capital-GDP ratio, and
energy, for both the PF and PS experiments, and compare them to data. Each time series is
scaled by its respective value in the last quarter of 1994 to emphasize the impact of the crisis.
The key result is that GDP, labor and capital fall more than twice as much in percentage
terms as in the data, under both expectation scenarios. This is true, that is, whether or not
agents saw the crisis coming. In both experiments, GDP falls by 19.5% between the last
quarter of 1994 and the last quarter of 1995, compared with 9.8% in the data. The behavior
of energy is also very similar across experiments. The yearly fall in predicted energy in 1995
is similar to the fall in the data.17
The two experiments make very diﬀerent predictions for the behavior of output and
inputs before the crisis. In the PF experiment, the capital-output ratio falls before 1995
as agents anticipate the crisis. This makes all variables fall in anticipation of the large
changes in exogenous variables in 1995. Series predicted by the PS experiment track their
empirical counterparts more closely as agents base their investment decisions on optimistic
expectations.
To measure the relative role of each of the many shocks that hit the Mexican economy in
1995, we carried out PF experiments in which only one of the exogenous variables changes
after the last quarter of 1994, while other variables remain constant at their values in the
last quarter of 1994. We ﬁnd that changes in the capital tax and the labor tax have little
eﬀect on the behavior of GDP in 1995. Shocks to the consumption tax, interest rates and the
price of energy yield more pronounced falls in output: -2.9%, -2.2% and -1.4% during 1995
respectively.18 The impact of TFP outweighs that of all other shocks combined. Holding
other exogenous variables at their end-of-1994 values, TFP alone would have caused GDP
16

Dotsey and Mao (1992) ﬁnd that the accuracy of linear approximation methods worsens as the variance
of shocks rises.
17
Energy falls much more on impact than in the data, but this owes in large part to our assumption that
nominal prices remained constant in 1995 which we have to make for lack of quarterly data.
18
We take into account the fact that keeping the interest rate ﬁxed at its (high) value in the last quarter
of 1994 induces a trend in endogenous variables. Results are reported net of this trend.

to fall by 15.4% in 1995 relative to 1994. The magnitude of the TFP shock accounts for the
model’s counterfactually large fall in output. The benchmark model’s diﬃculties in matching
the behavior of output and inputs during Mexico’s 1995 crisis do not stem from ﬁscal shocks.

3.4

Sensitivity analysis

This section evaluates the robustness of the previous ﬁndings to our assumptions on preferences.
Elasticity of labor supply
Our ﬁndings are sensitive to the assumed elasticity of the labor supply on the part of
households. In particular, a higher ν would render labor supply less elastic, which should
reduce the predicted fall in hours worked, hence in output in 1995. In fact, it is clear that
one can ﬁnd a value for ν such that the model will predict the correct fall in hours worked
during the crisis. Figure 4 shows that setting ν = 4.33, which is at the upper bound of the
estimates available for the United States, produces a fall in hours in 1995 that resembles
quantitatively the fall in the data, in a PF experiment.19 The same is true for the behavior
of GDP. Hours worked fall 2.5% in the data and 3.3% in the model. GDP falls 9.8% in
the data and 11.7% in the model. Additionally, the model predicts a recovery in GDP very
similar to the one observed, as can be seen on the graph. In fact, predicted and observed
GDP meet by the ﬁrst quarter of 2003.
However, such a value for ν predicts a counterfactually stable path for labor input outside
the crisis. The standard deviation of predicted hours before the crisis and over the full length
of our sample is quite smaller than in the data, as can be seen in the ﬁgure. The standard
deviation of labor predicted by the model between 1990 and 2003 is 0.004, smaller than the
actual value of 0.007. The volatility of predicted labor represents 57% of actual volatility.
In short, it is not possible to ﬁnd a value for ν such that the model yields a reasonable path
for hours worked both during and outside of the crisis period.

Greenwood et al. (1988) report estimates of the elasticity of labor supply. The value of ν = 4.33 is
implicit in the lowest estimate reported.

Standard preferences
Heretofore we have assumed preferences such that the wage elasticity of the labor supply
is exogenous and invariant over time. As we have mentioned, these preferences are typically
used in small open economy models because they improve the model’s consistency with business cycle regularities. It is interesting nonetheless to consider the impact of giving households preferences that are more standard in closed economy exercises. Speciﬁcally, assume
that households now order consumption and labor supply sequences {ct , lt }+∞
t=0 according to
the following intertemporal utility function:
+∞

β t {log ct + ρ log(1 − lt )} ,

t=0

where ρ > 0 measures the weight of leisure in utility. Households face the same budget
constraint as before. Solutions to the household problem must satisfy, for all t:
β(1 + τtc )
ct+1
k
=
(1 + rt+1 (1 − τt+1
))
c
ct
1 + τt+1
ρct
wt (1 − τtl )
=
.
1 − lt
1 + τtc

(3.4)
(3.5)

Both conditions have the usual interpretation. The ﬁrst says that the marginal rate of substitution between consumption in two consecutive periods must equal the return on savings
(the marginal rate of transformation between date t and date t + 1 consumption). The
second equates the marginal utility of leisure in each period to its opportunity cost, the
net wage times the marginal utility of consumption. Using ﬁrst order conditions for proﬁt
maximization by ﬁrms (those are unchanged), (3.5) can be rearranged to read:

lt =

(1 + τtc )ρct
1+
(1 − τtl )αn yt

−1
(3.6)

Condition (3.6) shows how standard preferences could help account for the behavior of hours
worked in 1995. Hours worked are now a simple function of the consumption-output ratio.
If the model predicts a fall in consumption comparable in relative size to the fall in output

in 1995, the model will also predict little change in hours, as in the data.20
Computing the model requires solving for paths of consumption, hours worked, assets and
capital that satisfy (3.4), (3.6), the household’s budget constraint, and the same diﬀerence
equation in capital as before. In implementing the algorithm described in appendix B, we
set ρ to match the average level of hours worked before the crisis. We also choose the initial
level of asset a0 so that the model implies an approximate debt to GDP ratio of 35% for
Mexico in 1994, as in the data.21 To match the fact that hours have no trend before 1995,
we set the rate of time preference to the average net interest before the crisis, and set long
term interest rates accordingly in our two expectation scenarios.
The model with standard preferences performs very poorly under perfect foresight, for
obvious reasons. In this model, consumption rises at the after-tax rate of interest net of
the rate of time preference. Since interest rates are very high in 1995, consumption rises
throughout the year (see equation (3.5)) while TFP falls markedly. Correspondingly, the
consumption-output ratio rises markedly and hours worked fall even more drastically than
in the previous model. Those results are available upon request.
Under perfect surprise assumptions however, agents adjust consumption in the ﬁrst quarter of 1995 after discovering the true path of exogenous series. In particular, consumption
must be adjusted downward since agents realize that their future income will be much lower
than expected. This could mitigate the negative impact on hours worked. In fact, as ﬁgure 5
shows, the consumption-output ratio actually falls, so that hours rise in the ﬁrst quarter.22
But this eﬀect is short-lived, as consumption then starts rising steeply due to high interest
rates. Hours adjust downward and eventually bring output, hours and capital markedly
below trend. In other words, once agents have adjusted to the crisis, hours and output and
input series fall below their data counterpart.
The basic problem is that given persistently high interest rates after the crisis, the model
predicts that consumption should rise faster than output, and that, correspondingly, hours
20

For consistency with the model, we measure consumption as the sum of private consumption, the returns
and depreciation of durable goods, the returns to government capital, and government consumption minus
Indirect Business Taxes.
21
This is approximately the value reported in Lane and Milesi-Ferretti (2001).
22
We replace the energy panel of the ﬁgure with the consumption-output ratio path since this is the crucial
statistic in this model.

should fall for several periods, which is at odds with the evidence. If one sets the rate of time
preference to oﬀset the high interest rates that prevail after the crisis, predicted hours trend
steeply up before the crisis when interest rates are relatively low, which is also at odds with
the evidence. This a manifestation of the diﬃculties standard preferences present for open
economy models. Because interest rates are volatile and display large, persistent deviations
from their average values in economies such as Mexico, predicted consumption and hours
worked display counterfactually large ﬂuctuations.

Factor utilization

The fact that the predictions for inputs deviate drastically from their empirical counterparts
suggest that factor hoarding could play a big role during crises. In this section, we use
standard models of factor utilization to quantify the importance of capital utilization and
labor hoarding.

4.1

Capital utilization

Consider a small open economy model with variable capital utilization modeled as in Greenwood, Hercowitz and Huﬀman (1988). Household preferences are the same as in the benchmark model. Firms can now alter the rate at which they utilize capital. Raising utilization in
a given period raises output, but it also raises the quantity of capital lost to depreciation.23
Speciﬁcally, depreciation at date t depends on utilization ut as follows:
δt =

uφt
,
φ

where φ > 1. Output at date t is now given by:

αk
nαt n eαt e .
ztu ut ktf
23

Gertler, Gilchrist and Natalucci (2003) also combine the framework in Greenwood et al. (1988) with a
small open economy model.

Firms continue to take all prices as given and choose ktf , nt, et and ut each period to maximize:

αk
nαt n eαt e +
ztu ut ktf

uφ
1− t
φ

ktf − ktf 1 + rtk − nt wt − et pet .

This maximization problem yields the following condition for optimal utilization at date t:
yt
αk
kt

ut =

φ1
,

(4.1)

as in Greenwood, Hercowitz and Huﬀman (1988). That is, the capital-output ratio path
implies a unique utilization path. Given measures of the capital to output ratio and a value
for φ, TFP net of changes in capital utilization can then be computed as:
ztu =

yt
.
(ut kt ) nαt n eαt e
αk

While no further adjustment to national accounts data is needed to implement those calculations, the capital stock needs to be recalculated, because its evolution depends on utilization
in each period. The capital stock and the utilization rate need to be calculated recursively.
Using an initial capital stock and a value for φ we calculate utilization as deﬁned by condition
(4.1). Then next period’s capital stock can be calculated using the following law of motion:

kt+1 = kt

uφ
1− t
φ

+ it ,

where it is gross capital formation net of adjustment costs. Proceeding recursively yields a
path of capital, utilization and therefore of TFP adjusted for utilization. Implementing this
procedure requires a value for φ, the curvature of the depreciation schedule. Simple algebra
shows that in this model the steady state depreciation rate is equal to

r
φ−1

where r is the

steady state rate of interest. We choose φ = 1.44 to imply a steady state yearly depreciation
rate of 8% (the constant depreciation rate we assumed in the benchmark model), assuming
that interest rates eventually become constant at their last value in our sample.24 We also
24

This value for φ is close to values used in studies of the U.S. economy. Greenwood et al. (1988) use
φ = 1.42 to imply a steady state yearly depreciation rate of 10%. Burnside and Eichenbaum (1996) estimate

experimented with diﬀerent values of φ, including a value such that the implied steady state
depreciation rate is 5% on a yearly basis. The quantitative results are practically the same
in all cases.
Because our measure of the capital-output ratio falls in 1995, utilization does as well. This
makes intuitive sense. TFP in the ﬁrst quarter of 1995 falls by a large amount while interest
rates (the opportunity cost of capital) increase signiﬁcantly. This gives ﬁrms an incentive to
postpone the consumption of capital services. Speciﬁcally, we ﬁnd that measured utilization
fell 5.7% between the last quarter of 1994 and the last quarter of 1995. This implies that
adjusted TFP falls less than unadjusted TFP (5.1% versus 7.1%), as shown in ﬁgure 6. Note
however that it continues to fall by a large amount. In fact, relative to movements outside
of the crisis period, the 1995 change in adjusted TFP is as much of an outlier as the change
in unadjusted TFP.
The key question is whether making capital utilization endogenous improves the ability
of the model to account for the behavior of output and inputs. To answer that question, we
ﬁrst recalibrate parameters to continue matching our calibration targets. Figure 7 plots the
predictions of the model for GDP, labor, capital and utilization, under the PS scenario.25
The results are quantitatively similar to those we obtained in the benchmark model.
GDP, labor, and capital fall much more than in the data in 1995. In particular, GDP falls
by 22.5%, even though adjusted TFP falls less than unadjusted TFP. The reason for this
is simple. When confronted with exogenous shocks, ﬁrms can adjust labor and energy as
before, but they can also vary capital utilization. This new margin of adjustment magniﬁes
the economy’s response to productivity shocks.26 The predicted fall in utilization in 1995
(8.5% in the PS experiment) is higher than in the data as the model predicts a greater
increase in the capital-output ratio than in the data. Finally, like in the benchmark model,
TFP and the interest rate shock account for most of the fall in output. Experiments in
which taxes and the price of energy are held constant at their pre-1995 level produce a fall
φ to be 1.56 in the U.S.
25
We do not show the results of the PF experiment to reduce clutter. Results are very similar to those we
obtained with the benchmark model.
26
This is consistent with the ﬁndings of Burnside and Eichenbaum (1996). They ﬁnd that the response of
the economy to a given productivity shock is magniﬁed once variable capital utilization is introduced in a
real business cycle model.

in output that continues to markedly exceed its data counterpart. For instance, GDP falls
by 19.9% between 1994 and 1995 in the PF case when ﬁscal variables are held constant.
In summary, including variable capital utilization helps account for some of the variance
of TFP but does not improve the performance of the model during 1995. The model continues
to predict that output and inputs should fall at least twice as much as observed in 1995.

4.2

Labor hoarding

Assume now that ﬁrms and households can use another margin of adjustment when confronted with exogenous shocks: eﬀort. We model labor hoarding in the spirit of Burnside
et al. (1993).27 Time devoted to work by households is indivisible: employed households
devote time f > 0 to work while unemployed households devote no time to work. As in
Hansen (1985) and Rogerson (1988), we convexify the choice set of households by allowing
them to randomize between employment and unemployment. Speciﬁcally, households choose
a probability lt of working in a given period, a level cet of consumption when employed, a
level cut of consumption when unemployed, and a level

of eﬀort when employed. We further

assume that working entails a ﬁxed cost κ > 0.28 Households maximize:
+∞

t=0

lt log

cet

1
− κ − (f t )ν
ν

+ (1 −

lt ) log (cut )

With this utility function, eﬀort is independent of consumption and income, as labor supply
was in the benchmark model. This makes the model with labor hoarding comparable to the
benchmark model in the sense that the short-run wage elasticity of aggregate labor supply
is governed by exogenous parameter ν > 1, and is independent of income and consumption.
We further assume as Burnside et al. (1993) that adjusting labor between periods is costly,
although our speciﬁcation of the cost is diﬀerent from theirs. Burnside et al. (1993) assume
that it takes one period to adjust employment. This constraint would never bind in the
perfect foresight case and would only bind in the ﬁrst quarter of 1995 in the perfect surprise
27

Baxter and Farr (2001) construct a two-country model with utilization modeled as in this paper and
with labor hoarding as in Bils and Cho (1994).
28
If there is no such cost, it is eﬃcient for households to work in every period, because they can adjust
their labor eﬀort in response to exogenous shocks. See Burnside et al. (1993).

case. We assume instead that households who change their work probability from lt to lt+1
in period t + 1 bear costs

ψl
(l
2 t+1

− lt )2 where ψl > 0.29 This speciﬁcation is similar to the

one used by Cogley and Nason (1995). As in the case of capital in the benchmark model,
assuming that adjustment costs are borne by households rather than by ﬁrms is immaterial
but simpliﬁes the exposition by keeping the ﬁrm’s problem static. Output in this model is
given by

where

f
t

αk
αn
yt = ztu,e ut ktf
eαt e ,
nt f ft
is the ﬁrm’s eﬀort choice, and nt is the fraction of households that they employ. In

equilibrium, nt = lt and

f
t

for all t. In appendix C, we show that optimal behavior on

the part of ﬁrms and households in this environment imply the following condition for eﬀort
in equilibrium:
t

αn (1 − τtl )yt
(1 + τtc )nt f

ν1
.

(4.2)

Note that eﬀort depends negatively on both the tax on labor and the tax on consumption.
Calibrating ν is diﬃcult since independent evidence on this parameter is not available. We
choose to experiment with various values centered around ν = 1.5, the value we used for
the curvature of the disutility of labor in the benchmark model. The ﬁxed length of work
f is set to 0.45. This number corresponds to average hours per worker before 1995, relative
to approximate discretionary time available in a quarter, 1300 hours. These parameters are
suﬃcient to infer eﬀort from the observed path of hours worked nt f and output. Figure
6 shows the behavior of adjusted TFP when ν = 1.5.30 Combined, capital utilization and
eﬀort account for 90% of the fall in TFP in 1995. Note that factor hoarding accounts for
much of the variance of TFP outside of the crisis as well.
We now ask whether including eﬀort improves the consistency of the model with evidence.
To that end, we need to assign values to a few more parameters. In all experiments we choose
κ to match the initial level of employment in our sample. Following our previous calibration
strategy, the natural way to choose a value for employment adjustment cost parameter ψl
29

Without adjustment costs, one easily shows that the optimal level of eﬀort is constant across periods.
Results for a variety of other values of ν are available upon request. Reducing ν increases the elasticity
of eﬀort, and eﬀort accounts for a greater share of the variance of TFP when ν is low. At the same time,
for all values of ν considered, eﬀort accounts for a large fraction of the volatility of TFP, both during and
outside of the crisis.
30

is to match the standard deviation of employment before the crisis. However, we found
that doing this led to unreasonably large ﬂuctuations in employment after the crisis. To
keep employment within reasonable bounds, we choose a value of ψl such that nt remains
between 40% and 60% throughout the simulation period in all experiments. One should bear
in mind this calibration compromise when interpreting our results.
The predictions of the model in the perfect surprise case are shown in ﬁgure 8 for the
case ν = 1.5. Hours worked are very smooth, like capital, which is not surprising since their
evolution is governed by a similar second order diﬀerence equation, and labor adjustment
costs are set high.31 In particular, hours worked now fall less than observed in 1995: 2.0%
versus 2.5%. Because hours fall very little, GDP falls much less than in previous experiments
during the crisis. Predicted GDP falls slightly more than observed GDP: 10.0% versus 9.8%.
The model predicts paths for the capital-output ratio and output-employment ratio very
similar to the ones observed. Consequently, predicted utilization and eﬀort track closely the
ﬂuctuations of observed counterparts. Energy falls signiﬁcantly more than in the data in
the ﬁrst quarter of 1995, as in the previous experiments. But the relatively good behavior
of the model during 1995 is short-lived. As labor slowly adjusts, GDP remains below its
data counterpart and eventually diverges from it by magnitudes quite similar to what we
obtained in the benchmark economy. The eventual real impact of the crisis is just as large
as in the previous models. We also found that varying ν does not change results much.32
Finally, we carried out a PS experiment in which taxes and the energy price remain
constant at their pre-1995 average values, assuming ν = 1.5. In sharp contrast to previous
experiments, the real impact of the crisis becomes smaller than observed when only interest
rates and TFP are allowed to ﬂuctuate as in the data after 1994. Predicted GDP falls less
than observed: 5.2% versus 9.8% between 1994 and 1995.
31

Even though the resulting value of ψl is high, employment adjustment costs represent a small fraction
of gross output, at most 0.5% in any given period.
32
Results are available upon request. The overall impact of the crisis generally rises with ν as the elasticity
of eﬀort falls.

Conclusion

In this paper, we document the fact that TFP falls by very unusual magnitudes after ﬁnancial
crises, and argue that these falls pose a serious challenge for the standard small open economy
model. In the case of Mexico’s Tequila crisis, the benchmark model predicts that inputs and
output should have fallen at least twice as much in percentage terms as they did. Standard
models of endogenous factor utilization suggest that factor hoarding can account for much
of the fall of TFP during the crisis. However, we ﬁnd that this does not solve the output
puzzle. The factor hoarding models we study also predict that output should fall much more
than it does following ﬁnancial crises.
Our paper focuses for the most part on the Mexican case, but we provide some evidence
that TFP fell by a very unusual amount during recent crises in Asia, a fact that is ignored
by most quantitative studies of these episodes. Falling capital utilization may explain some
of the real impact of these crises, as argued by Gertler et al. (2003), but like in the case of
Mexico, this is unlikely to account for the behavior of output. More generally, we interpret
our results as suggesting that a full understanding of the real impact of ﬁnancial crises will
require some modeling of the allocation of resources across sectors. For example, employment
started growing briskly in the export sector in Mexico after the devaluation in 1994. The
fall in output could reﬂect transitory losses in the quality of labor as employees devote time
to learning new skills.
Finally, our ﬁndings have implications for the potential ability of the neoclassical growth
model to account for depression episodes in Latin American nations. Kydland and Zarazaga
(2002) use a closed economy version to account for Argentina’s recent economic history. The
most challenging time period for the model begins with Argentina’s 1989 crisis, and extends
past Argentina’s 1995 crisis. The model predicts that investment should have fallen much
more than it did in 1989, and recovered much faster than it did thereafter. Similarly, the
results in Bergoeing et al. (2002) show that a closed economy model’s predictions diverge
from the evidence around Mexico’s Tequila crisis. Output and especially labor fall much
more than observed in 1995. Recent depression periods in Latin American are best described
as series of ﬁnancial crises. The closed economy neoclassical growth model’s diﬃculties in
24

accounting for the behavior of output, the capital-output ratio and hours worked in those
countries likely stems from the fact that it does not account well for the real impact of
ﬁnancial crises.

Mexican data appendix

This appendix describes how we construct empirical counterparts for theoretical variables
with Mexican data. We use quarterly data when available, and impute quarterly series from
yearly series otherwise. Our sample goes from 1980.1 to 2003.1. Data from original sources
are seasonally adjusted using the Census Bureau’s X12-Arima procedure. All data are in
1993 prices. The following quarterly series are available from Mexico’s Instituto Nacional de
Estadı́stica, Geografı́a e Informática (INEGI) and Mexico’s Central Bank (detailed sources
are available upon request):
1. Gross Domestic Product (GDP)
2. Gross Fixed Capital Formation, private (GFCFp)
3. Gross Fixed Capital Formation, public (GFCFg)
4. Change in inventories (CH)
5. Private Gross Capital Formation (GCFp)=GFCFp+CH
6. Gross Capital Formation=GCFp+GFCFg
7. Purchases of durable goods by households.
In our model there is no energy producing sector. A ﬁrst step towards making the variables
in the data consistent with theoretical ones is to eliminate the energy sector from the national
accounts. There are no quarterly series for GDP or investment in the energy sector. INEGI
provides GDP data at yearly frequency in 1993 prices for the oil and electricity sectors
between 1988 and 2001. To construct quarterly data, we multiply quarterly GDP by the
yearly ratio of the energy sector’s GDP to overall GDP. For years before 1988 and after 2001
we use the ratio’s average between 1988 and 2001. Yearly data for investment in the oil
industry is available from INEGI for the 1980-2002 period, and after 1987 for the electricity
sector. As in the case of GDP, we use yearly ratios of investment in the energy sector to
overall investment to construct a quarterly series after 1987. For years before 1987 and after
2000 we assume that the ratio is equal to the value observed in 1987. We use the 1987 value
rather than the post-1987 average because the ratio decreases from 1987 on.
In order to make GDP from national accounts consistent with output in our model, we
need to construct a few more quarterly variables: Indirect business taxes (IBT), the returns
of government capital, the returns and depreciation of the stock of durable goods, and energy
expenditures by ﬁrms outside of the energy sector. IBT data are available from INEGI only
at yearly frequency, and we use yearly ratios as above to impute quarterly data.
25

Using data on private and public investment, and purchases of durable goods, we construct three capital stock series using the perpetual inventory method.33 We assume a yearly
depreciation rate of 6% for private capital, 5% for government capital and 20% for durable
goods. To construct the stock of total capital, we add up the three resulting stocks. The
average yearly depreciation rate implied by the total stock of capital, total investment and
the law of motion of capital in the benchmark model is 8%. To calculate gross returns to
government capital and the stock of durables we assume a net yearly return of 4% and the
same depreciation rates as above.
Quarterly energy consumption data come from INEGI.34 Consumption numbers for the
non-energy producing sector for gas licuado (LPG), combustóleo (fuel oil), diesel, and gasolina
(gasoline) are based on internal sales (ventas internas) plus imports into Mexico. This quantity approximates consumption by all sectors other than the energy-producing sector. The
residential and public sectors were removed using weights inferred from annual consumption
data available from the Secretarı́a de Energı́a (SENER). Quarterly electricity data from INEGI include only the industrial sector, so we used annual industrial electricity consumption
as a percentage of total business sector consumption from SENER to impute consumption
by the rest of the business sector. All the series were converted to megajoules.
To obtain an energy price index, prices for diﬀerent types of energy are necessary. Electricity prices are average prices charged by the public sector to the industrial sector (Precios
Promedio de Energı́a Eléctrica del Sector Eléctrico Paraestatal ). Oil related product prices
are the prices charged in Mexico (Precios Internos de los Principales Productos) as reported
by INEGI. After converting the prices per unit for the diﬀerent types of energy into a common unit (pesos/megajoule), consumption numbers were used to calculate a weighted price
index, which was then converted into real terms using the GDP deﬂator. We use this index
to calculate expenditure on energy by ﬁrms outside of the energy sector.
After constructing these variables, we calculate the data counterpart of gross output in
our model by subtracting from GDP indirect business taxes and the energy sector’s GDP,
and adding the imputed returns and depreciation of government capital and durable goods.
Given that output in the model includes the expenditure on energy by ﬁrms, we also add this
variable to GDP. To calculate per capita variables we use the yearly series for population of
age 15 to 64 reported in Bergoeing, Kehoe, Kehoe and Soto (2002). To construct quarterly
working age population, we take yearly growth rates of population and calculate implicit
quarterly rates.
We also need an empirical counterpart for labor input in the model. To that end, we
ﬁrst calculate (seasonally adjusted) average hours worked in the manufacturing sector from
Mexico’s Manufacturing Sector Survey available from INEGI. The survey produces monthly
series for man-hours and for employment. There are two versions of the survey. The ﬁrst one
has data from 1987.01 to 1995.12. The second one has data starting in 1994.01. We splice the
33
We assume that gross capital formation data includes the empirical counterpart of theoretical adjustment
costs. In our simulations, adjustment costs amount to at most 0.9% of GDP in the benchmark model in any
given period.
34
In the process of producing these data, we discovered several errors in the electricity series published
by INEGI, including the fact that they did not reﬂect the eﬀects of major tariﬀ changes in 1992. We are
most grateful to Rafael del Villar from Banco de México and Jorge Garcia Peña from CFE for helping us
construct the correct series. INEGI has now updated and corrected its series.

quarterly hours per employee of the two surveys. To calculate a measure of workers relative
to total working age population, we multiply quarterly measures of the ratio of economically
active population relative to population of age 12 and higher by the employment rate and
by the fraction of employment in sectors other than the mining and electricity industries.
These data are available from INEGI. The measure of the labor input per working age
person consistent with the model is hours per employees times the ratio of employed persons
to population. We scale the resulting series by 1300, an approximation of the total number
of hours of discretionary time available in a quarter.

Computational appendix

Benchmark model
Simple manipulations of ﬁrst-order conditions for proﬁt and utility maximization show
that output can be reduced to a function of capital, so that equation (3.3) is a second
order diﬀerence equation in capital only. We assume that after the ﬁrst quarter of 2003 all
exogenous variables stay forever at their level in the ﬁrst quarter of 2003. Given k0 , we look
for the unique k1 such that the economy eventually converges to steady state via a standard
shooting algorithm. All endogenous variables can then be calculated as a function of the
path of physical capital. In the perfect surprise (PS) experiment, the algorithm is re-started
in the ﬁrst quarter of 1995 using as initial value for capital the value agents would choose
under the expectations assumed before 1995.
Standard preferences
Given parameter values and paths for exogenous shocks, the algorithm we use consists
of the following steps:
1. Guess a0 , the initial stock of risk-free bonds held by households.
2. Guess yc00 and calculate n0 . Since k0 is known and e0 = αe yp0e from the ﬁrm’s ﬁrst order
0
conditions, y0 can be calculated using the deﬁnition of output. So then can c0 .
3. Get c1 from (3.4).
4. Guess k1 and get y1 and n1 using (3.6) and the deﬁnition of output.
5. For t ≥ 0 obtain ct+2 and kt+2 inductively by repeating steps 2 and 3.
6. Iterate on k1 until path for capital is stable (i.e. variables converge to steady state
values).
7. Update

c0
y0

until path for assets is stable.

8. Update a0 until the debt-GDP ratio predicted by the model for 1994 is 35%, as in the
data.

Capital utilization
The model produces the same second order diﬀerence equation for capital as before,
except that output and depreciation now depend on utilization. But utilization is a function
of the capital-output ratio (see equation 4.1). Therefore, (3.3) can be written as a second
order diﬀerence equation in capital only as in the benchmark model, and the same shooting
algorithm can be used.
Labor hoarding
The algorithm is much more demanding in this case because one needs a simultaneous
solution to two second-order diﬀerence equations: one for capital as before, and one for
employment. Given initial values (k0 , n0 ) for capital and labor, we carry out the following
steps:
1. Guess a full path {nguess
}Tt=0 for employment where T is a large number.
t
2. Choose k1 so that, given the labor guess, the path predicted by the second order
diﬀerence equation for capital is stable.
3. Find n1 so that given the path for capital obtained in step 2, the path for labor
predicted by (C.6) is stable.
4. Iterate until the paths for labor and capital are approximately invariant
In the perfect surprise experiment, the algorithm is re-started in the ﬁrst quarter of
1995 using as initial value for capital and employment the values agents would choose under
optimistic expectations before 1995.

Labor hoarding model

Assume as in the text that households maximize:

+∞

1
ν
t
e
u
β lt log ct − κ − (f t ) + (1 − lt ) log (ct )
ν
t=0
where t is eﬀort at date t, lt is the probability that a household becomes employed, cet
is consumption if the household is employed, and cut is consumption if the household is
unemployed. Assuming quadratic labor adjustment costs and letting wt be the price of labor
services, households now face budget constraint:
(lt cet + (1 − lt ) cut ) (1 + τtc ) + kt+1 + at+1

ψ
ψl
= lt f t wt 1 − τtl +at (1+rt 1 − τtk )+kt (1+rtk 1 − τtk )− (kt+1 − kt )2 − (lt+1 − lt )2 +Tt .
2
2
In Hansen (1985) or Rogerson (1988), it is optimal for agents to equate consumption across
employment states. In our model this is not the case. It remains true that households equate
28

utility across employment states at all dates t:
cet − κ −

1
(f t )ν = cut .
ν

(C.1)

This implies that employed households consume more than unemployed households. Similarly, utility maximization by households implies that employment and eﬀort solve:
t wt (1

k
− τtl ) + ψl (1 + rt+1 (1 − τt+1
))(lt+2 − lt+1 ) = (cet − cut )(1 + τtc ) + ψl (lt+1 − lt )
wt (1 − τlt )
.
(f t )ν = t
1 + τct

(C.2)
(C.3)

On the other hand, proﬁt maximization by ﬁrms implies:
wt =

αn yt
.
nt f t

(C.4)

Equations (C.1-C.4), the fact that nt must equal lt in all periods, and some algebra imply
the following condition for eﬀort:
t

αn (1 − τtl )yt
(1 + τtc )nt f

ν1
.

(C.5)

Finally, ﬁrst order conditions for proﬁt maximization together with equations (C.1-C.4) yield
the following second-order diﬀerence equation for employment:

1 − τtl
κ
1 yt+1
c
αn 1 −
(nt+1 − nt )(1 + rt+1 (1 − τtk )) +
(1 + τt+1
). (C.6)
nt+2 = nt+1 +
ψn
ν nt+1
ψn

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Output

Hours

Capital

TFP

33
1
0.95
0.9
0.85
1990

0.95

0.9

0.85
1990

2000

1.05

1995

1.1

1990

1.1

2000

0.7

1995

0.8

1990

0.9

0.9
1990

0.9

2000
1

1995

0.95

0.9
1990

0.95

1.05

1.1

1990

0.8

0.8
2000

0.9

1995

1990

1.1

Mexico

1995

South Korea

2000

0.85
1990

0.9

0.95

1.05

1.1

1990

0.7

0.8

0.9

0.9
1990

0.95

1.05

1.1

1990

0.8

0.9

1.1

Figure 1: Output, inputs and TFP during recent ﬁnancial crises

1995

Thailand

2000

0.9
1990

1.1

1.2

1.3

1.4

1.5

0.92
1990

0.94

0.96

0.98

1.02

1.04

1994

1996

1998

2000

2002

1992

1994

1996

1998

2000

2002

Relative price of energy, 1994.4=1

1992

Benchmark TFP, 1994.4=1

2004

0.06
1990

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.005
1990

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

1992

τc
τl
k
τ

1992

1994

1998

1996

1998

Tax rates

1996

2000

2002

Interest rate at quarterly rates

Figure 2: Exogenous shocks during Mexico’s Tequila crisis

2004

35
2000

2002

2004

2002

2004

1990

0.6

0.6
2000

0.7

1998

0.8

1996

0.9

1994

1990

1.1

1990

1.2

1992

1998

Labor

1996

0.6

1.2

1990

0.6

1994

0.8

1992

0.9

0.7

1.1

Data
PF
PS

1.2

GDP

1992

Figure 3: Predictions of the benchmark model

1994

1998

1996

1998

Energy

1996

2000

Capital to GDP ratio

2002

2004

36
2000

2002

2004

2002

2004

1990

0.6

0.6
2000

0.7

1998

0.8

1996

0.9

1994

1990

1.1

1990

1.2

1992

1998

Labor

1996

0.6

1.2

1990

0.6

1994

0.8

1992

0.9

0.7

Data
ν=4.33

1.1

0.7

1.2

GDP

1992

1994

1998

1996

1998

Energy

1996

2000

Capital to GDP ratio

Figure 4: Benchmark model with low elasticity of labor supply

2002

2004

37
2000

2002

2004

2000

2002

2004

1990

0.6

0.6
1998

0.7

1996

0.8

1994

0.9

1992

1990

1.1

1990

1.2

Labor

1998

1.2

1990

1996

0.7

1994

0.8

1992

0.9

0.6

1.1

Data
PS

1.2

GDP

1992

Figure 5: Logarithmic preferences

1996

1998

2000

1994

1996

1998

2000

Consumption to output ratio

1994

Capital to GDP ratio

2002

2004

0.92
1990

0.94

0.96

0.98

1.02

1.04

1992

1994

1996

1998

2000

2002

2004

Benchmark
Capital utilization
Capital utilization and effort

Figure 6: TFP adjusted for endogenous capital utilization and labor hoarding

39
2000

2002

2004

2002

2004

1990

0.6

0.6
2000

0.7

1998

0.8

1996

0.9

1994

1990

1.1

1990

1.2

1992

1998

Labor

1996

0.6

1.2

1990

0.6

1994

0.8

1992

0.9

0.7

Data
PS

1.1

0.7

1.2

GDP

1992

1994

1998

1996

1998

Utilization

1996

2000

Capital to GDP ratio

Figure 7: Predictions of model with endogenous capital utilization

2002

2004

2000

2002

2004

2002

2004

1996

1998

2000

2002

2004

1990

0.6

1994

0.7

1992

0.8

1990

1
0.9

1.1

0.9

1.2

Utilization

1990

0.6

0.6
2000

0.7

0.7
1998

0.8

1996

0.9

1994

1990

1.1

1990

1.2

1992

1998

Labor

1996

0.6

1.2

1990

0.6

1994

0.8

1992

0.9

0.9
0.7

0.7

1.1

Data
PS

1.2

GDP

1992

1994

1998

1996

1998

Effort

1996

Energy

1996

2000

Capital to GDP ratio

Figure 8: Predictions of model with labor hoarding

2002

2004

Full text of Working Papers (Federal Reserve Bank of Dallas) : Financial Crises and Total Factor Productivity, Center for Latin American Economics Working Paper 0105

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