metadata: authors: 0: author: Hevia,Constantino
count: World
docna: 0: docna: Emerging market fluctuations : what makes
            the difference ?
docty: Policy Research Working Paper
theme: Micro, Small and Medium Enterprise support
majtheme: Financial and private sector development
subtopic: Consumption,Fiscal & Monetary Policy,Labor & Employment Law,Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Labor Markets,Business Cycles and Stabilization Policies
teratopic: Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: Aggregate fluctuations in emerging
            countries are quantitatively larger and qualitatively
            different in key respects from those in developed countries.
            Using data from Mexico and Canada, this paper decomposes
            these differences in terms of shocks to aggregate efficiency
            and shocks that distort the decisions of households about
            how much to invest, consume, and work in a standard model of
            a small open economy. The decomposition exercise suggests
            that most of these differences are explained by fluctuations
            in aggregate efficiency, distortions in labor decisions over
            the business cycle, and, most importantly, fluctuations in
            country risk. Other distortions are quantitatively less important.
repnme: repnme: Emerging market fluctuations : what makes
            the difference ?
display_title: Emerging market fluctuations : what
            makes the difference
listing_relative_url: /research/2009/04/10428495/emerging-market-fluctuations-makes-difference
topicv3: Manufacturing Sectors m1326521 1281,Macroeconomic and Structural Policies
            m1327380 439,Population, Aging and Health m1327736 640,Working Age Population m1504053 2749,Labor Supply m1504055 2751
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 42
author_keys: 0: author_key: 955277
model_extractions: WPS4897 Policy ReseaRch WoRking PaPeR 4897 Emerging Market Fluctuations What Makes the Difference? _Constantino Hevia_ The World Bank Development Research Group Macroeconomics and Growth Team April 2009
Policy ReseaRch WoRking PaPeR 4897

# **Abstract**

Aggregate fluctuations in emerging countries are quantitatively larger and qualitatively different in key respects from those in developed countries. Using data from Mexico and Canada, this paper decomposes these differences in terms of shocks to aggregate efficiency and shocks that distort the decisions of households about how much to invest, consume, and work in a standard model of a small open economy. The decomposition exercise suggests that most of these differences are explained by fluctuations in aggregate efficiency, distortions in labor decisions over the business cycle, and, most importantly, fluctuations in country risk. Other distortions are quantitatively less important.

This paper—a product of the Growth and the Macroeconomics Team, Development Research Group—is part of a larger effort in the department to understand macroeconomic volatility in developing countries. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at chevia@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Emerging Market Fluctuations: What Makes the Dierence?<sup>_∗_</sup>

## Constantino Hevia<sup>_†_</sup>

> _∗_ JEL Codes: E32, F41. Keywords: Business Cycles, Small Open Economy, Country Risk Premium

> _†_ I thank Aart Kray, Juan Pablo Nicolini, Demian Pouzo, Claudio Raddatz, and Luis Serven for helpful comments and suggestions. The ndings, interpretations, and conclusions expressed in this paper are entirely those of the author. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent
# 1 Introduction

Aggregate uctuations in emerging countries are dierent from those in developed countries. Table 1 illustrates this point. The rst and second rows of the table display summary statistics of the business cycle in two representative emerging and developed countries, Mexico and Canada respectively. The third and fourth rows of the table report the same statistics averaged across 13 emerging and 13 developed countries. Overall, the table shows that, while economic aggregates are substantially more volatile in emerging countries (except, perhaps, hours worked), there is a deeper dierence between these countries: consumption is more volatile than output in emerging countries but less volatile in developed countries; and the share of net exports on output is highly countercyclical in emerging countries but less so in developed countries. Moreover, these regularities hold across a large number of emerging and developed countries (Neumeyer and Perri, 2005; Aguiar and Gopinath, 2007).

Table 1: Business Cycles in Emerging and Developed Small Open Economies

|Country/Moment|_σ_(_y_)|_σ_(_l_)|_σ_(_m/y_)|_σ_(_c_)_/σ_(_y_)|_σ_(_x_)_/σ_(_y_)|_ρ_(_m/y, y_)|
|---|---|---|---|---|---|---|
|Mexico|2_._12 (_._45)|1_._4 (_._2)|1_._63 (_._43)|1_._28 (_._05)|4_._51 (_._43)|_−_0_._80 (_._11)|
|Canada|1_._44 (_._21)|1_._69 (_._24)|0_._91 (_._1)|0_._85 (_._08)|4_._6 (_._23)|_−_0_._05 (_._24)|
|Emerging Countries|2_._74|_−_|3_._22|1_._45|3_._91|_−_0_._51|
|Developed Countries|1_._34|_−_|1_._02|0_._94|3_._41|_−_0_._17|

This table reports second moments of HP-ltered quarterly aggregate data. The statistics _σ_ ( _x_ ) and _ρ_ ( _x, y_ ) measure, respectively, the standard deviation of the series _x_ and the correlation coecient between the series _x_ and _y_ . The variable _y_ denotes output; _l_ , hours worked; _m_ , net exports; _c_ , private consumption; and _x_ , investment. GMM-based standard errors are reported in parentheses. Sources: Rows 1 and 2, author's calculations. Rows 3 and 4 taken from Aguiar and Gopinath (2007).

While researchers agree on these dierences, they disagree on their causes: by introducing dierent frictions and shocks into their models, researchers provide alternative stories for why aggregate uctuations in emerging countries are dierent. (Christiano, Gust, and Roldós, 2004; Neumeyer and Perri, 2005; Mendoza, 2008; Uribe and Yue, 2006; Aguiar and Gopinath, 1
2007; Arellano, 2008, to name but a few.) These frictions and shocks, however, are usually chosen based on intuition or anecdotal evidence.

The purpose of this paper is to identify the type of reduced form distortions that explain the observed business cycle dierences between emerging and developed countries. The logic of the experiment is as follows. At a conceptual level, shocks and frictions in most structural models drive a wedge between certain marginal rates of substitution and marginal rates of transformation relative to a prototype frictionless economy. Then, instead of testing whether a particular structural model generates the data, I estimate these wedges based on the prototype economy and measure their contribution to aggregate uctuations. The estimated wedges, however, cannot be used to identify primitive shocks and frictions: models with dierent primitive shocks and frictions could induce movements in the same reduced form wedge in the prototype economy. Nevertheless, these wedges oer useful information: a successful model should induce reduced form wedges similar to those estimated based on the prototype economy; moreover, these wedges should account, quantitatively, for uctuations in the economic aggregates.

Several authors have used variations of this approach applied to the U.S., including Parkin (1988), Hall (1997), Rotemberg and Woodford (1999), Mulligan (2002), Chari, Kehoe, and McGrattan (2007), and Shimer (2009). In this paper I follow more closely the methodology proposed by Chari, Kehoe, and McGrattan, labeled `Business Cycle Accounting'. In this methodology, the researcher interprets the data through the lens of a small open economy model. This prototype economy is subject to reduced form shocks that are interpreted literally as total factor productivity (the eciency wedge), as labor and investment taxes (the labor wedge and investment wedge), as uctuations in real interest rates (the risk premium wedge), and as government consumption (the government consumption wedge).

I estimate a stochastic process for these wedges using data from a representative emerging country, Mexico, and a representative developed open country, Canada. Next I estimate the realized wedges and study their contribution to aggregate uctuations in both countries.

2
Besides considering aggregate uctuations at the business cycle frequency, I also study two recession episodes: the 1995 Mexican crisis and the 1983 Canadian recession.

The main ndings of this paper are the following: rst, all wedges, except for the government consumption wedge, are substantially more volatile in Mexico; second, uctuations in the risk premium wedge explain the `deep' dierences between Mexico and Canada: the excess volatility of consumption over output and the highly countercyclical share of net exports on output in Mexico; third, the risk premium wedge plays, if anything, a secondary role in Canada's business cycle; fourth, the government consumption wedge has negligible eects in both countries; and nally, the investment wedge does not play any role in Mexico's uctuations but contributes somewhat to the behavior of aggregate investment and net exports in Canada.

Extending these results to the set of all emerging countriesthe empirical regularities discussed in Neumeyer and Perri (2005) and Aguiar and Gopinath (2007) imply that, in principle, we couldthese ndings suggest that, to build models of emerging market uctuations consistent with the data, researchers need to understand, rst and foremost, what type of primitive shocks and transmission mechanisms drive uctuations in the risk premium wedge, in the eciency wedge, and in the labor wedge.

On the methodological side, this paper departs from Chari, Kehoe, and McGrattan's procedure in using a dierent prototype economy to decompose uctuations and in proposing an alternative strategy to estimate the wedges. Chari, Kehoe, and McGrattan base their analysis on a prototype closed economy. This paper uses a model of an open economy. Although the open economy model is observationally equivalent to a prototype closed economy, an open economy is the natural framework to study uctuations in emerging countries. Indeed, a number of authors have explicitly introduced models with uctuations in the price of foreign debt, together with additional frictions, to understand emerging market uctuations (Neumeyer and Perri, 2005; Aguiar and Gopinath, 2006; Uribe and Yue, 2006; Arellano, 2008).

The paper is organized as follows. Section 2 discusses the prototype small open economy 3
and an observational equivalence. Section 3 describes the decomposition methodology. Section 4 applies the methodology using data from Mexico and Canada. Section 5 discusses the implications of the results for understanding emerging market uctuations and concludes.

# 2 A Prototype Small Open Economy

This section describes a standard small open economy model with incomplete asset markets augmented with ve stationary reduced form shocks, referred to as wedges. In the model, these reduced form shocks are interpreted literally as productivity shocks (the eciency wedge), as labor income and investment taxes (the labor wedge and investment wedge), as uctuations in interest rates (the risk premium wedge), and as government consumption (the government consumption wedge).

Time is denoted by _t_ = 0 _,_ 1 _,_ 2 _..._ and the state of the economy at period _t_ by _st_ . Let _s_<sup>_t_</sup> = _{s_ 0 _, s_ 1 _, ..., st}_ denote the history of the economy until time _t_ and _π_ ( _s_<sup>_t_</sup> ) the probability of observing the history _s_<sup>_t_</sup> as of time zero. Wedges in period _t_ depend on the history _s_<sup>_t_</sup> . The eciency wedge is denoted by _A_ ( _s_<sup>_t_</sup> ) ; the labor wedge, by (1 _− τl_ ( _s_<sup>_t_</sup> )) ; the investment wedge, by 1 _/_ (1 + _τx_ ( _s_<sup>_t_</sup> )) ; the risk premium wedge, by 1 _/Z_ ( _s_<sup>_t_</sup> ) , and the government consumption wedge, by _g_ ( _s_<sup>_t_</sup> ) . Note that a drop in any of these wedges is interpreted as an increase in the corresponding distortion.<sup>1</sup> A representative household has preferences over contingent sequences of consumption, _c_ ( _s_<sup>_t_</sup> ) , and hours worked, _l_ ( _s_<sup>_t_</sup> ) , represented by the expected utility function where 0 _< β <_ 1 is a subjective the discount factor and _η_ is the growth rate of the population. Here and throughout this section, all variables are expressed in per capita terms.

> 1While a drop in government expenditures may not mean an increase in any distortion, it does induce a drop in output.

4
Households own the stock of capital and are able to issue one period uncontingent discount bonds traded in international nancial markets. Each bond is a contract to deliver one unit of the consumption good in the following period in exchange of _q_ ( _s_<sup>_t_</sup> ) units today. I decompose the discount price as where _q_<sup>_⋆_</sup> ( _s_<sup>_t_</sup> ) is interpreted as the price of a risk-free bond and 1 _/Z_ ( _s_<sup>_t_</sup> ) as a risk premium factor. Fluctuations in _Z_ ( _s_<sup>_t_</sup> ) introduce a wedge between the intertemporal marginal rate of substitution between consumption today and tomorrow, and the marginal rate of transformation in an economy that faces the relative price _q_<sup>_⋆_</sup> ( _s_<sup>_t_</sup> ) .

The household has initial capital _k_ 0 = _k_ ( _s_<sup>0</sup> ) and outstanding foreign debt _b_ 0 = _b_ ( _s_<sup>0</sup> ) , and face the budget constraint Here _k_ ( _s_<sup>_t−_1</sup> ) is the stock of capital chosen in period _t−_ 1 and available for production in period _t_ , _b_ ( _s_<sup>_t−_1</sup> ) is the stock of foreign debt maturing at period _t_ , _x_ ( _s_<sup>_t_</sup> ) is investment, _w_ ( _s_<sup>_t_</sup> ) is the wage rate, _v_ ( _s_<sup>_t_</sup> ) is the rental rate of capital, _τx_ ( _s_<sup>_t_</sup> ) is a tax on investment expenditures, _τl_ ( _s_<sup>_t_</sup> ) is a labor income tax, and _T_ ( _s_<sup>_t_</sup> ) is a lump-sum transfer. Because the government has access to lump-sum transfers, I assume from now on, and without loss of generality, that all foreign debt is held by the household.

Competitive rms rent capital and labor from the household to produce consumption goods with the constant returns to scale technology where _γ_ is the rate of labor augmenting technical progress. These rms choose capital and 5
labor to maximize prots, given by Households own a technology to produce capital goods. After being used in the production of consumption goods, the stock of capital can be mixed with investment expenditures to produce capital goods in the following period according to the constant returns to scale production function<sup>2</sup> Feasibility in the nal good sector requires Here _g_ ( _s_<sup>_t_</sup> ) is government consumption and _m_ ( _s_<sup>_t_</sup> ) represents net exports, given by Standard small open economy models with exogenous world interest rates induce a unit root in the equilibrium quantities. Because the unit root complicates the numerical approximation of the equilibrium, the model is rendered stationary by imposing the following debt elastic discount price where _r_<sup>_⋆_</sup> is a world interest rate, _φ_ is the steady state debt to output ratio, and _ψ >_ 0 measures the sensitivity of the discount price to deviations in the debt to output ratio from _φ_ .<sup>3</sup>

> 2This specication allows for technologies with capital adjustment costs as well as the standard capital accumulation equation (1 + _η_ ) _k_ ( _s_<sup>_t_</sup> ) = (1 _− δ_ ) _k_ ( _s_<sup>_t−_1</sup> ) + _x_ ( _s_<sup>_t_</sup> ) , where _δ_ is a capital depreciation rate.

> 3Although there are several methods to induce stationarity, most of them imply similar business cycle

6
In equation (7), _b_ ( _s_<sup>_t_</sup> ) and _y_ ( _s_<sup>_t_</sup> ) refer to aggregate variables; therefore, the elasticity of the discount price to _b_ ( _s_<sup>_t_</sup> ) _/y_ ( _s_<sup>_t_</sup> ) is not internalized by the household. Nevertheless, when calibrating the model I set _ψ_ to 0 _._ 001 , which implies that movements in the debt to output ratio have a small eect on _q_<sup>_⋆_</sup> ( _s_<sup>_t_</sup> ) yet it is sucient to induce a unique steady state.

An equilibrium allocation of the prototype economy with initial conditions _k_ ( _s_<sup>0</sup> ) and _b_ ( _s_<sup>0</sup> ) is a path for output _y_ ( _s_<sup>_t_</sup> ) , consumption _c_ ( _s_<sup>_t_</sup> ) , labor _l_ ( _s_<sup>_t_</sup> ) , capital _k_ ( _s_<sup>_t_</sup> ) , foreign bonds _b_ ( _s_<sup>_t_</sup> ) , and investment _x_ ( _s_<sup>_t_</sup> ) that satises the technological constraint (3), the capital accumulation equation (4); the feasibility condition (5); the net exports equation (6), where _q_ ( _s_<sup>_t_</sup> ) satises (2) and (7); and the optimality conditions The term _π_ ( _s_<sup>_t_+1</sup> _|s_<sup>_t_</sup> ) is the probability of _s_<sup>_t_+1</sup> conditional on _s_<sup>_t_</sup> ; _Uc_ ( _s_<sup>_t_</sup> ) and _Ul_ ( _s_<sup>_t_</sup> ) are the marginal utility of consumption and labor; _Fk_ ( _s_<sup>_t_</sup> ) and _Fl_ ( _s_<sup>_t_</sup> ) are the marginal product of capital and labor in the nal goods technology; and _Gk_ ( _s_<sup>_t_</sup> ) and _Gx_ ( _s_<sup>_t_</sup> ) are the marginal product of capital and investment in the capital goods technology, all in history _s_<sup>_t_</sup> .

Equation (8) summarizes the intratemporal labor-consumption choice and the demand for labor, (9) is the intertemporal rst order condition with respect to foreign debt, and (10) summarizes the intertemporal Euler equation with respect to capital and the demand for capital.

dynamics (Schmitt-Grohé and Uribe, 2003).

7
# Observational Equivalence

The ve shocks of the previous model have a dubious structural interpretation. Indeed, few economists would agree that random labor or investment taxes are the main driving forces behind business cycle uctuations. In a recent paper, however, Chari, Kehoe, and McGrattan (2007) prove that a large class of structural models with interpretable primitive shocks and frictions induce reduced form wedges similar to those in the prototype economy. Specically, they show that we can nd a stochastic process for the wedges such that the equilibrium allocation of the structural model coincides with that of the prototype economy. Frictions and shocks in a particular structural model manifest themselves as variations in one or more wedges in the prototype economy.

The mapping from the class of models to the prototype economy, however, is not one to one. More than one model with frictions could induce variations in the same wedge in the prototype economy. Thus, we cannot identify individual models (and therefore, primitive shocks and frictions) from the data. We can, on the other hand, limit the set of models consistent with them: a model is not consistent with the data if its primitive shocks and frictions induce wedges in the prototype economy that do not contribute to observed uctuations. Equivalently, the identication of the wedges that contribute the most to observed uctuations can be used as a guide for building detailed models consistent with the data.

In a series of papers, Chari, Kehoe, and McGrattan (2002; 2005; 2007) prove the observational equivalence of several models and a prototype closed economy. A model with sticky wages (Bordo, Erceg, and Evans, 2000) and a model with cartelization and unionization (Cole and Ohanian, 2004) are equivalent to a prototype economy with labor wedges; the models with nancial frictions of Bernanke and Gertler (1989), Carlstrom and Fuerst (1997), Kiyotaki and Moore (1997), and Bernanke, Gertler, and Gilchrist (1999) induce investment wedges in the prototype economy; and models with input nancing frictions could induce labor wedges (Neumeyer and Perri, 2005; Mendoza, 2008), or eciency wedges (Christiano, 8
Gust, and Roldós, 2004; Mendoza, 2008). Because the prototype small open economy is observationally equivalent to Chari, Kehoe, and McGrattan's closed economy, all these equivalence results extend to the prototype small open economy.

Moreover, some of the above models also induce a risk premium wedge if we interpret them in terms of the prototype open economy: the model with a simple borrowing constraint discussed in Chari, Kehoe, and McGrattan (2005) induces risk premium and government consumption wedges in the prototype open economy; nancial frictions as in Kiyotaki and Moore (1997) and Mendoza (2008) induce investment and risk premium wedges in the prototype open economy; and disturbances in foreign interest rates as in Neumeyer and Perri (2005) and Uribe and Yue (2006) induce a risk premium wedge, and indirectly through input nancing frictions, a labor wedge in the prototype open economy.

# 3 The Decomposition of Business Cycles

Having discussed the prototype economy and the equivalence result, this section describes the decomposition methodology. The methodology starts by parameterizing and calibrating the model; next, I discuss how to estimate a stochastic process for the wedges and their realized values; and nally, I measure the contribution of the wedges to aggregate uctuations in Mexico and Canada by performing counterfactual experiments.

## Counterfactual Experiments

The Business Cycle Accounting methodology decomposes the movements in some economic aggregates in terms of movements in one or more wedges. To measure the contribution of the wedges to aggregate uctuations, I simulate counterfactual economies in which one or more wedges are active (they take their measured values), and the other wedges are inactive (they are set to constants).

The following experiment, for example, measures the contribution of the labor wedge to 9
aggregate uctuations. Suppose that we know the stochastic process followed by the state _st_ , we observe the history _s_<sup>_t_</sup> , and we know the mappings _A_ ( _s_<sup>_t_</sup> ) , _τl_ ( _s_<sup>_t_</sup> ) , _τx_ ( _s_<sup>_t_</sup> ) , _Z_ ( _s_<sup>_t_</sup> ) , and _g_ ( _s_<sup>_t_</sup> ) . I construct a counterfactual economy as follows: given the true stochastic process for _st_ and history _s_<sup>_t_</sup> , let the labor wedge be as in the actual economy, 1 _− τ_ ˆ _l_ ( _s_<sup>_t_</sup> ) = 1 _− τl_ ( _s_<sup>_t_</sup> ) , and ˆ map the other wedges to a constant, for instance, their values at time zero: _A_ ( _s_<sup>_t_</sup> ) = _A_ ( _s_<sup>0</sup> ) , ˆ ˆ _τx_ ( _s_<sup>_t_</sup> ) = _τx_ ( _s_<sup>0</sup> ) , _Z_<sup>ˆ</sup> ( _s_<sup>_t_</sup> ) = _Z_ ( _s_<sup>0</sup> ) , and _g_ ( _s_<sup>_t_</sup> ) = _g_ ( _s_<sup>0</sup> ) for all _t_ . The contribution of the labor wedge to aggregate uctuations is measured by comparing the time series generated by the counterfactual economy with the data. The contribution of the other wedges, in isolation or in combination, is measured in a similar way. Note that, in doing these counterfactual experiments, I change the mappings from _s_<sup>_t_</sup> to the wedges but keep both, the process followed by _st_ and its realized values, the same across experiments. We therefore need to identify _st_ and _π_ ( _s_<sup>_t_</sup> ) .

To identify _st_ and _π_ ( _s_<sup>_t_</sup> ) , I follow Chari, Kehoe, and McGrattan (2007) and assume that the state follows a ve dimensional stationary autoregressive process where _s_ ̄ is the mean of _st_ , _P_ is the matrix on lagged values, and _εt_ +1 is an i.i.d. Gaussian process with mean zero and covariance matrix _V_ ; thus, the history of shocks _s_<sup>_t_</sup> is summarized by the current state _st_ . To identify the state, I assume that there is a one to one mapping from the wedges in the prototype economy to _st_ . Since the observation of the wedges uniquely identies the state, let _st ≡_ (log _At, τlt, τxt,_ log _Zt,_ log _gt_ ) without loss of generality. Therefore, the problem of identifying _st_ is reduced to the problem of identifying the wedges.

# Parametrization and Calibration

Now I state the functional forms representing preferences and the production functions for consumption and capital goods. Next I discuss the calibration of the prototype economy.

10
Each period in the model represents one quarter. Preferences are given by where _σ >_ 0 , 0 _< ρ <_ 1 , and the time endowment is normalized to 1 . The production function for consumption goods is given by _AF_ ( _k, l_ ) = _Ak_<sup>_α_</sup> _l_<sup>1</sup><sup>_−α_</sup> and the one for capital goods by where _x/_ ̄ _k_<sup> ̄</sup> is the investment to capital ratio in a balanced growth path and _φ >_ 0 . Note that _G_ ( _k, x_ ) is a standard capital accumulation equation with quadratic adjustment costs. To solve for the equilibrium of the model, all variables dated _t_ are normalized by level of technology (1 + _γ_ )<sup>_t_</sup> . Normalized consumption, for example, is given by _c_ ( _s_<sup>_t_</sup> ) _/_ (1 + _γ_ )<sup>_t_</sup> .<sup>4</sup> Here and throughout the paper, a `bar' above a variable refers to its normalized steady state value.

The population and productivity growth rates _η_ and _γ_ , and the parameters _s_ ̄ , _P_ , and _V_ are country specic. The parameter _η_ is set at the average growth rate of the working age population; the parameter _γ_ , at the average growth rate of real output per workingage person; and the parameters _s_ ̄ , _P_ , and _V_ are estimated separately for Mexico and Canada. ̄ The element _s_ 4 = log _Z_<sup> ̄</sup> , however, is xed by a steady state condition.<sup>5</sup> A subset of the remaining parameters take standard values: the coecient of relative risk aversion is set at _σ_ = 2 ; the capital share in output, at _α_ = 0 _._ 32 ; the debt elasticity term, at _ψ_ = 0 _._ 001 (Schmitt-Grohé and Uribe, 2003; Aguiar and Gopinath, 2007); and the steady state

> 4The following are the exceptions: hours worked, _l_ ( _st_ ) , and the rental rate of capital, _v_ ( _st_ ) , are already stationary and need not be normalized; capital is normalized relative to the period in which it becomes available for production, _k_ ( _s_<sup>_t−_1</sup> ) _/_ (1 + _γ_ )<sup>_t_</sup> ; and debt is normalized relative to the period of maturity, _b_ ( _s_<sup>_t−_1</sup> ) _/_ (1 + _γ_ )<sup>_t_</sup> .

> 5Evaluating equation (7) at the steady state gives

If we insist that _φ_ =<sup> ̄</sup> _b/y_ ̄ , this equation determines _Z_<sup> ̄</sup> as a function of the parameters. Alternatively, we could allow for<sup> ̄</sup> _b/y_ ̄ = _φ_ ; then, as we estimate _Z_<sup> ̄</sup> , we use the previous equation to nd<sup> ̄</sup> _b/y_ ̄ . Unfortunately, the latter approach delivers highly counterfactual debt to output ratios (of about 300 percent). For this reason I follow the former approach, as does most of the literature, e.g. Aguiar and Gopinath (2007).

11
external debt to output ratio, _φ_ , is set at 50 percent in annual termsReinhart, Rogo, and Savastano (2003) report an average ratio of external debt to output of 44 percent for a group of emerging countries with some history of external default, 27 percent for a group of emerging countries with no history of default, and 54 percent for a group of industrial countries.

The remaining parameters are calibrated to match the average moments of a representative small open economy. In this economy, the population and productivity growth rates are 2 percent and 1 percent in annual terms; the world interest rate, _r_<sup>_⋆_</sup> , and average risk premium, log _Z_<sup> ̄</sup> , are 4 percent and 3 percent per year; the average eciency wedge is _A_<sup> ̄</sup> = 1 ; the labor and investment wedges are _τ_ ̄ _l_ = _τ_ ̄ _x_ = 0 ; the government wedge, _g_ ̄ , is chosen to match a ratio of government consumption to output of 15 percentthe average government consumption to output ratio is 10 percent in Mexico and 20 percent in Canada; the parameter _ρ_ is set to induce a steady state labor supply of 1 _/_ 3 ; the parameter _δ_ is chosen to induce a steady state investment to output ratio of 20 percentthe average investment to output ratio is 20.5 percent in Mexico and 21 percent in Canada; and the capital adjustment cost parameter _φ_ is set to induce an elasticity of the price of capital with respect to the investment to capital ratio of 25 percent (Chari, Kehoe, and McGrattan, 2007).<sup>6</sup> Table 2 summarizes these numbers.

# Estimation and Measurement of the Wedges

The parameters _s_ ̄ , _P_ , and _V_ of the process (11) are estimated using a maximum likelihood approach and data on output, investment, net exports, hours worked, and government consumption.

The data are quarterly observations on gross domestic product, aggregate investment, hours worked, net exports of goods and services, and government consumption expenditures. Data from Mexico covers the period 1987:12007:4; data from Canada, the period 1976:1

> 6Most papers in the literature calibrate the parameter _φ_ to match the volatility of aggregate investment generated by the model with the data. In the Business Cycle Accounting methodology, however, the model matches the data exactly for any value the parameters. Because it is not possible to follow the traditional approach, I set this number to induce an elasticity of the price of capital with respect to the investment to capital ratio similar to what is estimated for the U.S., 25 percent.

12
Table 2: Calibration of the Prototype Economy

|Description|Symbol|Value|
|---|---|---|
|Risk Aversion (preferences)|_σ_|2|
|Consumption exponent (preferences)|_ρ_|0_._32|
|Discount factor (preferences)|_β_|0_._987|
|Capital depreciation rate (annual)|_δ_|4_._7%|
|Capital exponent (technology)|_α_|0_._32|
|Capital adjustment cost|_φ_|13_._1|
|World interest rate (annual)|_r_<sup>_⋆_</sup>|4%|
|Debt elasticity term|_ψ_|0_._001|
|Steady state debt/output ratio (annual)|_φ_|50%|

The prototype economy is calibrated to match average moments of a representative small open economy.

2007:4. Hours worked is dened as average hours worked per worker in the manufacturing sector multiplied by total employment and divided by total hours available for work. The raw data were rst transformed into per working-age person; next, output, investment, net exports, and government consumption were exponentially detrended using the average growth rate of output per working-age person in each country. The sources and additional details on the construction of the data are described in Appendix A.

To estimate the parameters, the model is log-linearized around the steady state and the likelihood function is evaluated using the Kalman lter. (Appendix B describes the estimation procedure in detail.) There are 44 parameters to estimate: 4 in _s_ ̄ , 25 in _P_ , and 15 in _V_ because of the symmetry of the covariance matrix, only the lower triangular part of _V_ is estimated. The estimated coecients for Mexico and Canada are reported in Table 3.

The wedges are estimated after the maximum likelihood step. The government consumption wedge is observed directly. The labor wedge is measured using the condition that equates the marginal rate of substitution between consumption and labor with the marginal product of labor distorted by the labor tax rate. Introducing the proposed functional forms into (8) 13
and solving for 1 _− τl_ ( _s_<sup>_t_</sup> ) gives: Thus, the realized labor wedge is measured using the series of the consumption-output ratio and hours worked.

The eciency wedge is measured as a Solow residual: given a guess for the initial capital stock, _k_ ( _s_<sup>0</sup> ) , I construct a series for the stock of capital _k_ ( _s_<sup>_t_</sup> ) using investment data and the capital accumulation equation (4). Next, using the series of capital and data on output and hours worked, I obtain the eciency wedge _A_ ( _s_<sup>_t_</sup> ) as the residual in the output equation (3).

To measure the investment and risk premium wedges, I use the policy functions of the estimated model. Specically, these wedges are estimated using a xed-interval smoothing algorithm on the log-linearized model. A xed-interval smoother computes the expectation of an unobservable state in a model written in state space form, conditional on all the information contained in the sample (Hamilton, 1994; Anderson and Moore, 2005). As a by-product, the smoother computes the best estimates, in the mean squared error sense, of capital and debt at the initial period. (Mechanically, all wedges were estimated using the smoother.) Because there are ve wedges and ve observable variables, variations in the wedges explain all the movements in the data. Thus, the methodology decomposes uctuations in the ve observable variables in terms of ve wedges.

# 4 Results

This section applies the decomposition methodology to measure the contribution of the wedges (the eciency wedge, _At_ , the labor wedge, 1 _− τlt_ , the investment wedge, 1 _/_ (1 + _τxt_ ) , the risk premium wedge, 1 _/Zt_ , and the government consumption wedge, _gt_ ) to aggregate uctuations in Mexico and Canada. I start by considering general uctuations at the business cycle 14
Table 3: Estimated stochastic process for the wedges: Mexico and Canada<sup>a</sup>

|Means ̄_s_|M|atrix _P_|on lagg|ed value|s<br>Mat|rix _Q_, w|here _V_|=_QQ_|<sup>_′_b</sup>|
|---|---|---|---|---|---|---|---|---|---|
|A. Mexico <br><br>|estimates, <br>|1987:1|2007:4.|(Log-Lik|elihood= 18_._48)<br><br>|||||
|<br>0_._23<br>|<br>0_._92<br>|_−_0_._05|0_._08|1_._40|0_._02<br><br><br>1_._17|0|0|0|0<br>|
|<br>0_._29<br><br>|<br>_−_0_._01|0_._91|0_._04|0_._35|0_._02<br><br><br><br><br>_−_0_._08|1_._20|0|0|0<br><br>|
|<br>0_._19<br>|<br>_−_0_._06|0_._12|0_._79|_−_5_._65|0_._07<br><br><br>0_._83|_−_1_._06|1_._90|0|0<br>|
|<br>0_._007<br>|<br>0_._001|0_._01<br>|_−_0_._004|0_._87|_−_0_._002<br><br><br>_−_0_._09|0_._02|0_._00|0_._05|0<br>|
|<br>_−_2_._29<br>|<br>0_._56|0_._00|0_._03|3_._04|0_._62<br><br><br>0_._31|0_._03|0_._51|1_._45|2_._07<br>|
|B. Canada|estimates,|1976:1|2007:4.|(Log-Li|kelihood= 20_._41)|||||
|<br>0_._15<br>|<br>0_._88|_−_0_._01|_−_0_._03|1_._14|_−_0_._02<br><br><br>0_._76|0|0|0|0<br>|
|<br>0_._51<br><br>|<br>_−_0_._11|0_._95|_−_0_._07|0_._46|0_._00<br><br><br><br><br>0_._50|0_._57|0|0|0<br><br>|
|<br>_−_0_._25<br>|<br>_−_0_._04|_−_0_._05|0_._95|_−_0_._39|0_._02<br><br><br>0_._06<br>|_−_0_._39|0_._91|0|0<br>|
|<br>0_._009<br>|<br>0_._01|0_._01|0_._01|0_._83|0_._00<br><br><br>_−_0_._07<br>|_−_0_._01|_−_0_._01|0_._06|0<br>|
|<br>_−_1_._46<br>|<br>0_._05|_−_0_._13|_−_0_._13|_−_0_._10|0_._97<br><br><br>0_._08<br>|_−_0_._18|0_._50|_−_0_._28|1_._11<br>|

> a This table shows the estimated parameters of the stochastic process (11) for the wedges. The model is log-linearized around the steady state and the likelihood function is evaluated using the Kalman lter. The observable variables are output, investment, net exports, hours, and government consumption.

> b The entries of the matrix _Q_ are multiplied by 100 for easier reading.

frequency, and next I study two recession episodes: the 1995 Mexican crisis and the 1983 Canadian recession.

In summary, the results from this section can be described as follows. First, all wedges, except for the government consumption wedge, are substantially more volatile in Mexico. Second, uctuations in the risk premium wedge explain the `deep' dierences between Mexico and Canada: the excess volatility of consumption over output and the highly countercyclical share of net exports on output in Mexico. Third, the risk premium wedge has a negligible eect in Canada's business cycles, except to explain the volatility of net exports. Fourth, the government consumption wedge does not play any role in either country. And nally, the investment wedge has negligible eects in Mexico's uctuations, and only contributes to the behavior of investment and net exports in Canada.

15
# Decomposition of Business Cycles

Consider, rst, the properties of the estimated wedges. Tables 4 and 5 report some summary statistics of the estimated wedges in Mexico and Canada respectively.<sup>7</sup> Each table is divided into two panels. The top panel reports the standard deviation of the estimated wedges and the correlation of the wedges with each of the observable variables: output, consumption, investment, hours, and net exports. The lower panel reports the standard deviation of the wedges relative that of output and the correlation matrix of the estimated wedges.

Comparing the second column of the top panel of Table 4 with that of Table 5, we observe that, except for the government consumption wedge, all wedges in Mexico are substantially more volatile than in Canada: the eciency wedge by over 60 percent, the labor wedge by over 30 percent, the investment wedge by over 80 percent, and the risk premium wedge by 50 percent. Note that these magnitudes are in line with the volatility of output, which is almost 50 percent higher in Mexico (Table 1). These numbers, on the other hand, are somewhat dierent when measured relative to the volatility of output (second column of the lower panel of Tables 4 and 5). While the relative volatility of the eciency and investment wedges is higher in Mexico, the relative volatility of the labor wedge is higher in Canada, and the relative volatility of the risk premium wedge is similar in both countries.

Consider now the correlation of the wedges with the data. The upper panel of Table 4 shows that, in Mexico, output, consumption, investment, and hours worked are all positively correlated with the eciency wedge, with the labor wedge, with the risk premium wedge, and with the government consumption wedge. Output and consumption, however, are both negatively correlated with the investment wedge. In other words, these correlations suggest that downturns in Mexico are periods in which productivity is low, periods in which labor decisions and intertemporal consumption choices are relatively more distorted, but are periods

> 7In computing these numbers, the estimated wedges were rst HP-ltered with a smoothing parameter of 1600. GMM-based standard errors are reported in parentheses in these and all the tables that follow. The optimal weighting matrix is computed using the Newey-West estimator with a lag length equal to one fourth of the sample size.

16
in which investment decisions are relatively less distorted.

In Canada, on the other hand, the co-movements are somewhat dierent. First, the investment wedge is positively correlated with output and consumption, meaning that investment decisions are indeed relatively more distorted in downturns (upper panel of Table 5). Second, the risk premium wedge is virtually uncorrelated with output, consumption, and investment, but is negatively correlated with hours and net exports. Finally, and in contrast with Mexico, the government consumption wedge is positively correlated with output. This nding is consistent with the observation that scal policy is countercyclical in developed countries but procyclical in developing countries (Kaminsky, Reinhart, and Vegh, 2005).<sup>8</sup> The remainder of this section describes the contribution of the dierent wedges, both in isolation and in combination with other wedges, to aggregate uctuations in Mexico and Canada. Tables 6 and 7 display some summary statistics of the counterfactual economies with dierent active and inactive wedges. In reporting these results, I rst added an exponential trend equal to the sum of the estimated productivity and population growth rates to the counterfactual time series, and next I HP-ltered the resulting series. This transformation replicates the transformation applied to the data.

The counterfactual experiments are divided into models with one active wedge (panel A), models with two active wedges (panel B), and so on. The second and third columns provide a measure of how well the dierent models match output: the second column reports the relative standard deviation of counterfactual output to actual output and the third column measures the correlation between the two output series. If both of these numbers are close to one, the model ts output reasonably well. The last four columns report some summary statistic of the counterfactual series: the volatility of the share of net exports on output, the volatility of consumption and investment relative to that of output, and the correlation between output and the share of net exports on output. The rst row of these tables rewrites the summary

> 8The higher volatility of the risk premium wedge and its positive and signicant correlation with most economic aggregates in Mexico but not in Canada is consistent with the ndings in Neumeyer and Perri (2005) and Uribe and Yue (2006).

17
Table 4: Properties of estimated wedges in Mexico

||||Correl<br>|ation of wedg<br>|e with<br>||
|---|---|---|---|---|---|---|
|Wedge|_σw_|Output|Consumption|Investment|Hours|Net Exports|
|Eciency|1_._58 (_._26)|0_._92 (_._03)|0_._86 (_._05)|0_._73 (_._14)|0_._37 (_._17)|_−_0_._71 (_._13)|
|Labor|2_._35 (_._41)|0_._76 (_._08)|0_._83 (_._05)|0_._69 (_._08)|0_._86 (_._02)|_−_0_._79 (_._08)|
|Investment|2_._58 (_._33)|_−_0_._25 (_._15)|_−_0_._51 (_._13)|0_._21 (_._09)|0_._18 (_._11)|0_._19 (_._11)|
|Risk Prem.|0_._15 (_._03)|0_._75 (_._07)|0_._86 (_._04)|0_._63 (_._11)|0_._16 (_._17)|_−_0_._82 (_._06)|
|Govt. Cons.|0_._26 (_._03)|0_._41 (_._05)|0_._39 (_._04)|0_._19 (_._09)|0_._20 (_._07)|_−_0_._33 (_._07)|
||||Correlat|ion matrix of|wedges||
|Wedge|_σw/σy_|Eciency|Labor|Investment|Risk Prem.|Govt. Cons.|
|Eciency|0_._74 (_._04)|1|0_._51 (_._16)|_−_0_._37 (_._16)|0_._86 (_._04)|0_._41 (_._05)|
|Labor|1_._11 (_._08)||1|_−_0_._24 (_._10)|0_._50 (_._14)|0_._27 (_._07)|
|Investment|1_._22 (_._19)|||1|_−_0_._51 (_._10)|_−_0_._35 (_._07)|
|Risk Prem.|0_._07 (_._01)||||1|0_._26 (_._07)|
|Govt. Cons.|0_._12 (_._02)|||||1|

This table shows the properties of the estimated wedges in Mexico for the period 1987:12007:4. The estimated wedges are detrended using the Hodrick Prescott lter with smoothing parameter of 1600. The column _σw_ reports the standard deviation of the wedges, while _σw/σy_ reports the standard deviation of the wedges relative to the standard deviation of output. GMM-based standard errors are reported in parentheses

# statistics from Table 1.

In measuring the contribution of, say, the labor wedge to aggregate uctuations, two counterfactual economies are especially illustrative. In one economy, only the labor wedge moves as in the data and the other wedges are xed at their average values in the sample. In the other economy, the labor wedge is xed at its average value and the rest of the wedges move as in the data. The rst experiment measures the direct contribution of the labor wedge: the closer are the counterfactual time series to the data, the more important is the direct contribution of the labor wedge to aggregate uctuations. The second experiment measures the contribution of the labor wedge when combined with other wedges: the farther away are the predicted time series from the actual data, the more important is the contribution of the 18
Table 5: Properties of estimated wedges in Canada

||||Correl<br>|ation of wedg<br>|e with<br>||
|---|---|---|---|---|---|---|
|Wedge|_σw_|Output|Consumption|Investment|Hours|Net Exports|
|Eciency|0_._96 (_._10)|0_._61 (_._07)|0_._20 (_._14)|0_._35 (_._10)|_−_0_._08 (_._22)|0_._35 (_._08)|
|Labor|1_._76 (_._17)|0_._36 (_._25)|0_._75 (_._08)|0_._37 (_._21)|0_._81 (_._06)|_−_0_._46 (_._06)|
|Investment|1_._41 (_._18)|0_._67 (_._08)|0_._16 (_._16)|0_._91 (_._02)|0_._64 (_._11)|_−_0_._16 (_._15)|
|Risk Prem.|0_._10 (_._01)|0_._01 (_._10)|0_._12 (_._10)|0_._07 (_._12)|_−_0_._49 (_._09)|_−_0_._30 (_._07)|
|Govt. Cons.|0_._34 (_._03)|_−_0_._33 (_._12)|_−_0_._04 (_._15)|_−_0_._51 (_._06)|_−_0_._37 (_._13)|_−_0_._12 (_._09)|
||||Correlat|ion matrix of|wedges||
|Wedge|_σw/σy_|Eciency|Labor|Investment|Risk Prem.|Govt. Cons.|
|Eciency|0_._67 (_._16)|1|_−_0_._41 (_._23)|0_._23 (_._12)|0_._58 (_._10)|_−_0_._10 (_._13)|
|Labor|1_._23 (_._18)||1|0_._16 (_._19)|_−_0_._46 (_._08)|_−_0_._13 (_._16)|
|Investment|0_._98 (_._07)|||1|_−_0_._11 (_._07)|_−_0_._58 (_._04)|
|Risk Prem.|0_._07 (_._02)||||1|0_._30 (_._14)|
|Govt. Cons.|0_._24 (_._04)|||||1|

This table shows the properties of the estimated wedges in Canada for the period 1976:12007:4. The estimated wedges are detrended using the Hodrick Prescott lter with smoothing parameter of 1600. The column _σw_ reports the standard deviation of the wedges, while _σw/σy_ reports the standard deviation of the wedges relative to the standard deviation of output. GMM-based standard errors are reported in parentheses labor wedge, when combined with other wedges, to aggregate uctuations.<sup>9</sup> Consider, rst, counterfactual economies with only one active wedge. These experiments, displayed in panel A of Tables 6 and 7, suggest that only the eciency and labor wedges could account, by themselves, for an important fraction of output uctuations in both countries. The models with just the eciency wedge and just the labor wedge, however, completely miss the volatility of consumption and investment relative to that of output, and the negative correlation between output and the share of net exports on output in Mexico. Likewise, in Canada, the models with only eciency wedges and only labor wedges predict a large positive correlation between output and the share of net exports in output, and understate

> 9Because the government consumption wedge plays a negligible role in both countries, panels B and C of Tables 6 and 7 do not include experiments with the government consumption wedge.

19
the volatility of investment relative to that of output. These models, on the other hand, are consistent with the smaller volatility of consumption relative to that of output in Canada.

The investment, risk premium, and government consumption wedges, by themselves, cannot explain aggregate uctuations in either country. In Mexico, the economy with just the investment wedge accounts for only 10 percent of output volatility, grossly overstates the volatility of consumption and investment relative to that of output, and misses the negative correlation between output and the share of net exports on output. In the economy with just the risk premium wedge, predicted and actual output are negatively correlated, and the correlation of output with the share of net exports on output is extremely large. Finally, the economy with just the government consumption wedge accounts for only 4 percent of the output volatility and misses the volatility of the share of net exports on output and the correlation between output and the share of net exports on output. Likewise, in Canada, the model with just the investment wedge explains only 16 percent of the volatility of output and also completely overstates the volatility of consumption and investment relative to that of output. In the model with just the risk premium wedge, predicted output is negatively correlated with actual output, consumption is more volatile than output, and the correlation of output and the share of net exports on ouput is almost one. Finally, the model with just the government consumption wedge accounts for only 7 percent of the volatility of output.

Consider now counterfactual economies with all wedges but one. Panel D of Table 6 suggests that three wedges are essential to understand business cycles in Mexico: the eciency wedge, the labor wedge, and the risk premium wedge. Eliminating any of these wedges causes the model to miss the data in some dimension. In the model with no eciency wedges, predicted output is 54 percent less volatile than actual output and their correlation is just 0.53, investment is over eight times more volatile than output, and the correlation between output and the share of net exports on output is only -0.17. In the model with no labor wedges, predicted output is 43 percent less volatile than actual output and their correlation is only 0.41, the volatility of consumption and investment relative to that of output is overstated, and 20
Table 6: Contribution of the wedges to aggregate uctuations in Mexico

|Wedges/Moments|_σ_(_y_<sup>_o_</sup>)_/σ_(_y_)|_ρ_(_y_<sup>_o_</sup>_, y_)|_σ_(_m_<sup>_o_</sup>_/y_<sup>_o_</sup>)|_σ_(_c_<sup>_o_</sup>)_/σ_(_y_<sup>_o_</sup>)|_σ_(_x_<sup>_o_</sup>)_/σ_(_y_<sup>_o_</sup>)|_ρ_(_m_<sup>_o_</sup>_/y_<sup>_o_</sup>_, y_<sup>_o_</sup>)|
|---|---|---|---|---|---|---|
|Data|_−_|_−_|1_._63 (_._43)|1_._28 (_._05)|4_._51 (_._43)|_−_0_._80 (_._11)|
|A. Economies with|just one wedge||||||
|Eciency|0_._85 (_._05)|0_._89 (_._04)|1_._12 (_._18)|0_._71 (_._06)|1_._78 (_._26)|0_._48 (_._14)|
|Labor|0_._93 (_._05)|0_._83 (_._06)|1_._70 (_._31)|0_._34 (_._06)|0_._73 (_._09)|0_._95 (_._02)|
|Investment|0_._10 (_._01)|0_._46 (_._16)|1_._32 (_._19)|3_._01 (_._23)|32_._9 (4_._7)|0_._24 (_._09)|
|Risk Prem.|0_._66 (_._02)|_−_0_._91 (_._03)|3_._39 (_._71)|1_._01 (_._02)|4_._33 (_._13)|0_._99 (_._03)|
|Government|0_._04 (_._01)|0_._65 (_._08)|0_._23 (_._03)|1_._05 (_._05)|2_._67 (_._16)|0_._04 (_._20)|
|B. Economies with|two active wedg|es|||||
|Ec., Labor|1_._55 (_._03)|0_._99 (_._02)|1_._89 (_._52)|0_._40 (_._03)|0_._99 (_._07)|0_._95 (_._02)|
|Ec., Invest.|0_._88 (_._03)|0_._91 (_._04)|0_._68 (_._07)|0_._81 (_._12)|3_._33 (_._26)|0_._72 (_._03)|
|Ec., Risk Pr.|0_._57 (_._09)|0_._27 (_._07)|3_._65 (_._60)|2_._38 (_._35)|7_._41 (_._90)|0_._23 (_._08)|
|Labor, Invest.|0_._99 (_._06)|0_._83 (_._05)|2_._65 (_._35)|0_._46 (_._07)|3_._82 (_._61)|0_._77 (_._06)|
|Labor, Risk Pr.|0_._41 (_._08)|0_._41 (_._07)|1_._99 (_._48)|2_._00 (_._40)|7_._50 (1_._5)|_−_0_._26 (_._11)|
|Invest., Risk Pr.|0_._61 (_._03)|_−_0_._91 (_._03)|3_._12 (_._85)|0_._92 (_._02)|5_._91 (_._49)|0_._94 (_._03)|
|C. Economies with|three active wed|ges|||||
|E., Lab., Inv.|1_._60 (_._03)|0_._98 (_._03)|2_._20 (_._36)|0_._46 (_._06)|2_._05 (_._22)|0_._92 (_._03)|
|E., Lab., R. Pr.|0_._93 (_._02)|0_._99 (_._05)|2_._15 (_._38)|1_._53 (_._07)|4_._66 (_._19)|_−_0_._66 (_._05)|
|E., Inv., R. Pr.|0_._55 (_._08)|0_._36 (_._07)|2_._99 (_._07)|2_._16 (_._27)|7_._45 (1_._4)|0_._02 (_._13)|
|Lab., Inv., R. Pr.|0_._45 (_._07)|0_._487 (_._10)|2_._16 (_._56)|1_._63 (_._21)|8_._88 (1_._7)|_−_0_._12 (_._14)|
|D. Economies with|four active wed|ges|||||
|All but Eciency|0_._46 (_._07)|0_._53 (_._09)|2_._15 (_._60)|1_._58 (_._21)|8_._74 (1_._7)|_−_0_._17 (_._14)|
|All but Labor|0_._57 (_._09)|0_._41 (_._07)|3_._02 (_._70)|2_._15 (_._27)|7_._37 (1_._4)|_−_0_._02 (_._13)|
|All but Investment|0_._95 (_._02)|1_._00 (_._00)|2_._18 (_._39)|1_._51 (_._07)|4_._63 (_._18)|_−_0_._67 (_._04)|
|All but Risk Prem.|1_._62 (_._03)|0_._98 (_._03)|2_._19 (_._35)|0_._47 (_._06)|2_._00 (_._20)|0_._92 (_._02)|
|All but Government|0_._97 (_._00)|1_._00 (_._00)|1_._61 (_._43)|1_._30 (_._05)|4_._59 (_._42)|_−_0_._79 (_._12)|

This table reports the contribution of the wedges to aggregate uctuations in Mexico. For consistency when comparing the models with the data, the counterfactual series were exponentially retrended using the average population and output growth rates, and then detrended using the Hodrick Prescott lter with a smoothing parameter of 1600. The statistic _σ_ ( _x_ ) measures the standard deviation of the series _x_ , while _ρ_ ( _x, y_ ) measures the correlation coecient between the series _x_ and _y_ . Counterfactual time series are denoted with a superscript _o_ . The variable _y_ denotes output; _m_ , net exports; and _c_ , private consumption. GMM-based standard errors are reported in parentheses.

21
Table 7: Contribution of the wedges to aggregate uctuations in Canada

|Wedges/Moments|_σ_(_y_<sup>_o_</sup>)_/σ_(_y_)|_ρ_(_y_<sup>_o_</sup>_, y_)|_σ_(_m_<sup>_o_</sup>_/y_<sup>_o_</sup>)|_σ_(_c_<sup>_o_</sup>)_/σ_(_y_<sup>_o_</sup>)|_σ_(_x_<sup>_o_</sup>)_/σ_(_y_<sup>_o_</sup>)|_ρ_(_m_<sup>_o_</sup>_/y_<sup>_o_</sup>_, y_<sup>_o_</sup>)|
|---|---|---|---|---|---|---|
|Data|_−_|_−_|0_._91 (_._10)|0_._85 (_._08)|4_._60 (_._23)|_−_0_._05 (_._24)|
|A. Economies with|just one wedge||||||
|Eciency|1_._09 (_._23)|0_._61 (_._06)|1_._23 (_._11)|0_._64 (_._07)|0_._86 (_._07)|0_._93 (_._02)|
|Labor|0_._99 (_._16)|0_._32 (_._25)|0_._87 (_._10)|0_._78 (_._07)|1_._12 (_._05)|0_._77 (_._02)|
|Investment|0_._16 (_._01)|0_._11 (_._13)|1_._29 (_._17)|4_._53 (_._50)|22_._8 (1_._6)|_−_0_._17 (_._07)|
|Risk Prem.|0_._33 (_._07)|_−_0_._10 (_._22)|1_._01 (_._11)|1_._35 (_._20)|3_._70 (_._22)|0_._97 (_._00)|
|Government|0_._07 (_._01)|0_._59 (_._04)|0_._33 (_._02)|1_._08 (_._14)|3_._76 (_._50)|0_._14 (_._11)|
|B. Economies with|two active wedg|es|||||
|Ec., Labor|1_._07 (_._07)|0_._91 (_._04)|0_._88 (_._14)|0_._68 (_._06)|1_._17 (_._07)|0_._87 (_._04)|
|Ec., Invest.|1_._11 (_._24)|0_._61 (_._06)|1_._86 (_._14)|1_._00 (_._15)|3_._71 (_._69)|0_._54 (_._13)|
|Ec., Risk Pr.|1_._09 (_._27)|0_._58 (_._09)|1_._14 (_._12)|0_._54 (_._06)|1_._10 (_._06)|0_._92 (_._01)|
|Labor, Invest.|0_._96 (_._15)|0_._35 (_._24)|0_._90 (_._05)|0_._89 (_._10)|4_._01 (_._60)|0_._12 (_._29)|
|Labor, Risk Pr.|0_._93 (_._16)|0_._31 (_._21)|1_._29 (_._09)|0_._90 (_._07)|1_._93 (_._17)|0_._62 (_._04)|
|Invest., Risk Pr.|0_._42 (_._07)|_−_0_._04 (_._21)|1_._81 (_._21)|1_._80 (_._15)|10_._0 (1_._3)|0_._52 (_._08)|
|C. Economies with|three active wed|ges|||||
|E., Lab., Inv.|1_._06 (_._05)|0_._94 (_._03)|0_._71 (_._04)|0_._89 (_._07)|3_._92 (_._18)|_−_0_._01 (_._15)|
|E., Lab., R. Pr.|0_._96 (_._02)|0_._98 (_._00)|0_._86 (_._06)|0_._79 (_._04)|1_._69 (_._18)|0_._66 (_._07)|
|E., Inv., R. Pr.|1_._12 (_._27)|0_._57 (_._09)|1_._89 (_._20)|0_._82 (_._13)|3_._93 (_._85)|0_._51 (_._14)|
|Lab., Inv., R. Pr.|0_._92 (_._16)|0_._33 (_._19)|1_._50 (_._13)|1_._03 (_._10)|4_._71 (_._69)|0_._20 (_._22)|
|D. Economies with|four active wed|ges|||||
|All but Eciency|0_._93 (_._15)|0_._36 (_._19)|1_._54 (_._13)|1_._03 (_._05)|4_._74 (_._66)|0_._28 (_._20)|
|All but Labor|1_._16 (_._28)|0_._59 (_._09)|1_._80 (_._19)|0_._56 (_._08)|3_._94 (_._81)|0_._57 (_._13)|
|All but Investment|1_._00 (_._02)|0_._99 (_._00)|1_._10 (_._09)|0_._65 (_._06)|1_._56 (_._15)|0_._70 (_._07)|
|All but Risk Prem.|1_._08 (_._05)|0_._95 (_._02)|0_._56 (_._04)|0_._66 (_._03)|3_._94 (_._20)|0_._22 (_._09)|
|All but Government|0_._96 (_._01)|1_._00 (_._00)|0_._93 (_._10)|0_._98 (_._06)|4_._67 (_._25)|_−_0_._26 (_._24)|

This table reports the contribution of the wedges to aggregate uctuations in Canada. For consistency when comparing the models with the data, the counterfactual series were exponentially retrended using the average population and output growth rates, and then detrended using the Hodrick Prescott lter with a smoothing parameter of 1600. The statistic _σ_ ( _x_ ) measures the standard deviation of the series _x_ , while _ρ_ ( _x, y_ ) measures the correlation coecient between the series _x_ and _y_ . Counterfactual time series are denoted with a superscript _o_ . The variable _y_ denotes output; _m_ , net exports; and _c_ , private consumption. GMM-based standard errors are reported in parentheses.

22
the correlation of output with the share of net exports on output is zero. Finally, in the model with no risk premium wedges, predicted output is 62 percent more volatile than actual output, consumption is substantially less volatile than output, the volatility of investment relative to that of output is understated, and the share of net exports on output is highly procyclical. The investment and government consumption wedges, on the other hand, can be eliminated from the model without severely aecting the ability of the model to match the data. Interestingly, the investment wedge does not even contribute to the volatility of aggregate investment: the model with no investment wedges matches the volatility of investment relative to that of output remarkably well.

Panel D of table 7, on the other hand, suggest that two wedges are essential to understand business cycles in Canada: the eciency wedge and the labor wedge. There is, however, some role for the investment wedge and a small role for the risk premium wedge. The model with no investment wedges predicts a substantially lower volatility of investment compared to that in the data and a highly procyclical share of net exports on output; and the model with no risk premium wedges understate the volatility of the share of net exports on output.

Overall, these ndings suggest that business cycles in Mexico can be explained by the combined eect of the eciency wedge, the labor wedge, and the risk premium wedge. Moreover, the risk premium wedge is the key to understand the excess volatility of consumption over output and the highly countercyclical share of net exports on output. Business cycles in Canada, on the other hand, can be explained reasonably well by the combined eect of the eciency wedge and the labor wedge. The investment wedge contributes somewhat to the behavior of investment and net exports, and the risk premium wedge has, if anything, a secondary role.

# Two Recession Episodes

Now I apply the decomposition methodology to study two recession episodes: the 1995 Mexican `Tequila' crisis and the 1983 Canadian recession. In summary, the results of this section 23
are consistent with the ndings in the previous section with two exceptions: the investment wedge contributes to the recovery of output and labor in Canada, and the worsening in the risk premium wedge prevented an even larger drop in output and labor in Canada.

# The 1995 Mexican Crisis

The upper panel of Figure 1 shows output and the estimated wedges in the 1995 Mexican crisis. The series have been normalized to equal 100 at the beginning of the episode and the units of the risk premium wedge are shown on the right vertical axis. Output falls 12 percent in two quarters and remains below trend until 2000. The eciency, labor, and risk premium wedges deteriorate throughout the recession, although by 1998, the labor wedge fully recovers. The investment wedge, on the other hand, improves substantially throughout the episode, suggesting that investment decisions were, in fact, relatively less distorted during the Mexican crisis. The solid blue lines in Figure 2 display Mexican data. Labor (hours) is normalized to equal 100 at the beginning of the recession; investment and net exports are normalized by the initial level of output, and are shown in percentage points. Labor initially drops 3 percent but soon recovers, and by 1998 it is over 4 percent above its initial value. Investment drops abruptly and co-moves closely with output. Finally, net exports move sharply from a decit of 4 percent to a surplus of 4 percent and remain in surplus until 1998.

The contribution of the wedges to the Mexican crisis is shown in Figures 2 and 3. These gures report counterfactual experiments in which the active wedges are set to their estimated values and the inactive wedges are set at their values at the beginning of the crisis. Consider, rst, the direct contribution of the eciency wedge. The model with just the eciency wedge, shown in the upper panel of Figure 2, matches the evolution of output and labor remarkably well until 1997. Thereafter, the model predicts a somewhat slower recovery compared with that in the data. The model also misses the evolution of investment and net exports throughout the episode: predicted investment declines by a small amount and predicted net exports actually drops instead of increasing.

24
<!-- Start of picture text --> Mexico<br>120<br>Output<br>Efficiency Wedge<br>115 102<br>Labor Wedge<br>Investment Wedge<br>Risk−Prem. Wedge (right axis)<br>110<br>101<br>105<br>100 100<br>95<br>99<br>90<br>85 98<br>1995 1996 1997 1998<br>Canada<br>105<br>100 100<br>95<br>99<br>90<br>98<br>1982 1983 1984 1985<br>Risk−Premium Wedge<br>Risk−Premium Wedge<br><!-- End of picture text --> Figure 1: Output and four wedges in two recessions. (Data normalized to equal 100 before the recession; risk premium wedge is on left axis.) 25
Consider next the labor wedge. The model with just the labor wedge, also shown in the upper panel of Figure 2, predicts a fall in output of about one third of the fall in the data and a fall in labor larger than that in the data. This model captures the recovery and most ups and downs in output and labor, but also fails to match investment and net exports.

The models with just the investment wedge and with just the risk premium wedge, shown in the lower panel of Figure 2, cannot explain the crisis. The model with just the investment wedge completely misses the data: it predicts a steady increase in output and labor, and a small initial decline in investment followed by a strong increase since mid-1995. The model with just the risk premium wedge predicts an increase in output and labor, a small decline in investment, and a large increase in net exports. Note, however, that the risk premium wedge is the only wedge that, by itself, drives an increase in net exports.

Consider now economies with all wedges but one. In the model with no eciency wedge, displayed in the upper panel of Figure 3, predicted output actually increases and predicted labor uctuates until mid-1996 but matches the data closely thereafter. The model predicts an initial fall in investment of about two thirds of the fall in the data and matches its recovery almost perfectly thereafter. In addition, the model overstates the initial increase in net exports but matches that series closely after 1996. In other words, the eciency wedge contributes substantially to the behavior of output, to the initial decline in labor, and somewhat to the drop in investment. Note, however, that because this model predicts a recovery similar to that in the data (saving the level of output), it has to be that other wedges are mainly responsible for the recovery after 1996.

Consider now the model with no labor wedge, also shown in the upper panel of Figure 3. In this model, predicted output drops about half of the drop in the data and recovers faster that actual output does; predicted labor increases throughout the episode; predicted investment matches the data almost perfectly; and predicted net exports increase substantially more than actual net exports do. That is, the labor wedge contributes substantially to the behavior of output, labor, and net exports; and to the recovery since 1996.

26
<!-- Start of picture text --> Mexico<br>110 Output<br>Labor<br>110<br>105<br>105<br>100<br>100<br>95<br>95<br>90<br>90<br>85<br>1995 1996 1997 1998 1995 1996 1997 1998<br>35 Investment Net Exports<br>10<br>30<br>5<br>25<br>0<br>20<br>−5<br>15<br>−10<br>10<br>1995 1996 1997 1998 1995 1996 1997 1998<br>Model with Efficiency Wedge Model with Labor Wedge Data<br>Mexico<br>110 Output Labor<br>110<br>105<br>105<br>100<br>100<br>95<br>95<br>90<br>90<br>85<br>1995 1996 1997 1998 1995 1996 1997 1998<br>35 Investment Net Exports<br>10<br>30<br>5<br>25<br>0<br>20<br>−5<br>15<br>−10<br>10<br>1995 1996 1997 1998 1995 1996 1997 1998<br>Model with Investment Wedge Model with Risk−Premium Wedge Data<br><!-- End of picture text --> Figure 2: Data and counterfactual models with one wedge.

27
<!-- Start of picture text --> Mexico<br>110 Output Labor<br>110<br>105<br>105<br>100<br>100<br>95<br>95<br>90<br>90<br>85<br>1995 1996 1997 1998 1995 1996 1997 1998<br>35 Investment Net Exports<br>10<br>30<br>5<br>25<br>0<br>20<br>−5<br>15<br>−10<br>10<br>1995 1996 1997 1998 1995 1996 1997 1998<br>Model with No Efficiency Wedge Model with No Labor Wedge Data<br>Mexico<br>110 Output Labor<br>110<br>105<br>105<br>100<br>100<br>95<br>95<br>90<br>90<br>85<br>1995 1996 1997 1998 1995 1996 1997 1998<br>35 Investment Net Exports<br>10<br>30<br>5<br>25<br>0<br>20<br>−5<br>15<br>−10<br>10<br>1995 1996 1997 1998 1995 1996 1997 1998<br>Model with No Investment Wedge Model with No Risk−Premium Wedge Data<br><!-- End of picture text --> Figure 3: Data and counterfactual models with four wedges.

28
Now consider the model with no risk premium wedge, shown in the lower panel of Figure 3. This model predicts a drop in output and labor substantially larger that those in the data; a drop in investment about half of the drop in the data, and a large drop in net exports. In addition, this model does not match the behavior of consumption either (not shown in these gures). In other words, the risk premium wedge contributes substantially to the Mexican crisis. While its contribution to the behavior of output and labor is important, the most important role of the risk premium wedge is in the behavior of net exports: without that wedge, the model is unable to explain the large increase in net exports and the behavior of consumption.<sup>10</sup> Consider, nally, the model with no investment wedges. The plots in the lower panel of Figure 3 show that shutting down the investment wedge does not aect the ability of the model to match output, labor, and net exports. Because the model with no investment wedges cannot explain the full drop in investment and its recovery, I conclude that, if anything, the investment wedge only contributes to the behavior of investment in the Mexican crisis.

Summarizing, these ndings are consistent with those of the previous section and suggest that the eciency wedge, the labor wedge, and the risk premium wedge account for most of the aggregate behavior in the Mexican 1995 crisis. Moreover, among all wedges, only the risk premium wedge is able to account for the behavior of net exports in the Mexican crisis.

# The 1983 Canadian Recession

Now I apply the decomposition methodology to the 1983 Canadian recession. The lower panel of Figure 1 displays output and the estimated wedges in that episode. Output drops by 9 percent at the trough of the recession. There is a small decline in the eciency wedge, which

> 10The large drop in output and labor in the model with no risk premium wedges is likely to disappear if I change the period utility function and adopt the preferences proposed by Greenwood, Hercowitz, and Human (1988). With these preferences, changes in interest rates do not have a wealth eect on labor supply; therefore, the worsening in the risk premium wedge need not imply an increase in hours and, therefore, in output. These preferences, however, are inconsistent with a balanced growth path unless one assumes that the disutility of work increases at the growth rate of technology, an undesirable feature in preferences.

29
returns to trend by 1984. The labor wedge worsens substantially and tracks output closely. The investment wedge also follows output closely until 1984; afterwards, output recovers but the investment wedge does not. The risk premium wedge, on the other hand, remains at until mid-1983; then it worsens slightly but recovers by the second quarter of 1984. The solid blue lines in Figure 4 displays Canadian data. Investment and labor co-move closely with output, although investment recovers more slowly than output does. Net exports, on the other hand, increase from 0 to over 4 percent and remain in surplus for several years.

Consider rst counterfactual economies with only one active wedge. The upper panel of Figure 4 shows the prediction of the models with just the eciency wedge and just the labor wedge. The model with the eciency wedge alone misses the drop in output, labor, and investment, and predicts a small decline in net exports. The model with just the labor wedge matches hours remarkably well and accounts for about two thirds of the drop in output. This model, however, misses investment and net exports. The model with just the investment wedge, shown in the lower panel of Figure 4, completely misses output and labor, but matches investment and net exports reasonably well. Finally, the model with just the risk premium wedge predicts an increase in output, an increase in labor, misses the behavior of investment, but matches net exports well.

Consider now models with all wedges but one. The top panel of Figure 5 displays the predictions of the models with no eciency wedge and with no labor wedge. The lower panel of that gure shows the models with no investment wedge and no risk premium wedge. The model with no eciency wedge matches labor, investment, and net exports closely, but predicts a somewhat smaller decline and slower recovery in output compared with those in the data. The model with no labor wedge completely misses output and labor, matches investment closely, and overstates the increase in net exports. The model with no investment wedge matches output and labor closely, although it predicts a somewhat faster recovery than that in the data. This model, on the other hand, misses the behavior of investment and net exports. Consider, nally, the model with no risk premium wedge. This model misses net 30
<!-- Start of picture text --> Canada<br>105 Output 105 Labor<br>100 100<br>95 95<br>90 90<br>1982 1983 1984 1985 1982 1983 1984 1985<br>30 Investment Net Exports<br>10<br>25<br>5<br>0<br>20<br>−5<br>15<br>−10<br>1982 1983 1984 1985 1982 1983 1984 1985<br>Model with Efficiency Wedge Model with Labor Wedge Data<br>Canada<br>105 Output 105 Labor<br>100 100<br>95 95<br>90 90<br>1982 1983 1984 1985 1982 1983 1984 1985<br>30 Investment Net Exports<br>10<br>25<br>5<br>0<br>20<br>−5<br>15<br>−10<br>1982 1983 1984 1985 1982 1983 1984 1985<br>Model with Investment Wedge Model with Risk−Premium Wedge Data<br><!-- End of picture text --> Figure 4: Data and counterfactual models with one wedge.

31
<!-- Start of picture text --> Canada<br>105 Output 105 Labor<br>100 100<br>95 95<br>90 90<br>1982 1983 1984 1985 1982 1983 1984 1985<br>30 Investment Net Exports<br>10<br>25<br>5<br>0<br>20<br>−5<br>15<br>−10<br>1982 1983 1984 1985 1982 1983 1984 1985<br>Model with No Efficiency Wedge Model with No Labor Wedge Data<br>Canada<br>105 Output 105 Labor<br>100 100<br>95 95<br>90 90<br>1982 1983 1984 1985 1982 1983 1984 1985<br>30 Investment Net Exports<br>10<br>25<br>5<br>0<br>20<br>−5<br>15<br>−10<br>1982 1983 1984 1985 1982 1983 1984 1985<br>Model with No Investment Wedge Model with No Risk−Premium Wedge Data<br><!-- End of picture text --> Figure 5: Data and counterfactual models with four wedges.

32
exports and predicts a larger drop in output and labor, and a somewhat smaller decline in investment compared with those in the data.

Overall, these ndings suggest that most of the drop in output and labor is due to the labor wedge; the eciency wedge has a somewhat smaller role; the investment wedge accounts for the behavior of investment and somewhat for the recovery; and the slight worsening in the risk premium wedge in 1983-1984 acted to avoid a larger drop in output and laborsee, however, the discussion in footnote 10.

# 5 Discussion and Conclusion

In this paper I have decomposed uctuations in Mexico and in Canada in terms of reduced form shocks that drive a wedge between certain marginal rates of substitution and marginal rates of transformation relative to a prototype frictionless economy. I have found that the business cycle and the 1995 crisis in Mexico can be explained, to a large extent, by the combined eect of the eciency wedge, the labor wedge, and the risk premium wedge. And what is most important, the risk premium wedge accounts for the large increase in net exports in the 1995 crisis, the excess volatility of consumption over output, and the highly countercyclical share of net exports on output in Mexico. Business cycles in Canada, on the other hand, are mostly driven by uctuations in the eciency wedge and in the labor wedge.

Investment wedges do not contribute at all to uctuations in Mexico, not even to uctuations in aggregate investment. Moreover, the investment wedge is countercyclical and improved substantially during the 1995 crisis. In other words, investment decisions in Mexico are less distorted in downturns and more distorted in booms relative to a frictionless economy. In Canada, on the other hand, the investment wedge is procyclical and contributes somewhat to the behavior of aggregate investment and net exports.

If Mexico is, indeed, a representative emerging country and Canada a representative developed small open country, these ndings have implications for model development. Successful 33
models of emerging market uctuations should generate the type of wedges that we observe in the data, and these wedges should account, quantitatively, for aggregate uctuations. Thus, we need to understand what type of primitive shocks and transmission mechanisms drive uctuations in the risk premium wedge, in the eciency wedge, and in the labor wedge. Moreover, because a successful model should also induce countercyclical investment wedges, the transmission mechanisms and the spillovers from the primitive shocks to the wedges should be strong enough to mitigate the countercyclical eect of the investment wedge.

There are models consistent with some of these requirements. The working capital requirement on labor demand stressed by Neumeyer and Perri (2005), Uribe and Yue (2006), and Mendoza (2008); and on imported inputs, stressed by Mendoza (2008), translates shocks to the interest rate into labor and eciency wedges respectively. The problem is that in those models uctuations in interest rates are exogenous and, therefore, the issue of why the risk premium wedge in Mexico is dierent from that in Canada is left unexplained. The paper by Mendoza, however, also includes a collateral constraint that, when binding, induces an endogenous risk premium wedge that amplies the labor and eciency wedges induced by the working capital constraints. Moreover, as Chari, Kehoe, and McGrattan (2005) show, a tightening in the collateral constraint could manifest itself as an improvement in the investment wedge, which is, in fact, observed in the Mexican crisis. Still, in periods in which the collateral constraint is slack, Mendoza's model reduces to a model with exogenous uctuations in interest rates. These uctuations need to be understood. A step in that direction are the endogenous default models of Aguiar and Gopinath (2006) and Arellano (2008). These models, however, are still at an early stage of development and are either endowment or labor only economies; it is not clear if full-blown versions of these models will be consistent with all the business cycles facts.

This paper can be extended in a number of directions. The most obvious is to apply the methodology to other emerging countries and check whether the results are robust. The problem here is with the length of the time series and the large number of parameters that need to be estimated. Because most emerging countries do not have suciently long time 34
series, the estimates of the 44 parameters will likely be inaccurate. Note, however, that the similarity of the business cycle within the group of emerging countries suggests that the most important results will remain intact.

A second possibility is to extend the framework along the lines of Aguiar and Gopinath (2007). In that paper, they argue that the most important dierence between emerging and developed countries lies in the persistence of the total productivity shocks they face. Emerging countries, they claim, are mostly subject to trend shocks, while developed countries are mostly subject to temporary shocks. It is possible to extend the prototype economy along these lines by posing two types of eciency wedges, one temporary and one permanent. With this extension we could study whether the dierences between emerging and developed countries are due to the dierent type of productivity shocks they face, to dierent risk premium wedges, or to both. This extension, however, could be dicult to implement because the number of parameters to estimate increases by 50 percent, making the maximization of the likelihood functionalready challenging in the present formulationsubstantially more dicult.<sup>11</sup>

> 11The number of parameters to estimate increases to 63: 6 means, 36 coecients in the matrix on lagged values, and 21 coecients in the covariance matrix.

35