metadata: authors: 0: author: Comin, Diego
1: author: Loayza, Norman
2: author: Pasha, Farooq
3: author: Serven, Luis
count: World
docna: 0: docna: Medium-term business cycles in developing countries
docty: Policy Research Working Paper
theme: Analysis of economic growth
majtheme: Economic management
subtopic: Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Trade Policy,International Trade and Trade Rules,Energy Demand,Energy and Environment,Energy and Mining,Business Cycles and Stabilization Policies
teratopic: Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: Empirical evidence - including the
            current global crisis - suggests that shocks from advanced
            countries often have a disproportionate effect on developing
            economies. Can this account for the fact that aggregate
            fluctuations are larger and more persistent in the latter
            than in the former economies? And what are the mechanisms at
            play? This paper addresses these questions using a model of
            an industrial and a developing economy trading goods and
            assets, with (i) a product cycle shaping the range of
            intermediate goods used to produce new capital in each
            country, and (ii) investment adjustment costs in the
            developing economy. Innovation by the advanced economy
            results in new intermediate goods, at first produced at
            home, and eventually transferred to the developing economy
            through direct investment. The pace of innovation and
            technology transfer is driven by profitability. This process
            of technology diffusion creates a medium-term connection
            between both economies, over and above the short-term link
            through trade. Calibration of the model to match
            Mexico-United States trade and foreign direct investment
            flows shows that this mechanism can explain why shocks to
            the United States economy have a larger effect on Mexico
            than on the United States itself, and hence why Mexico shows
            higher volatility than the United States; why business
            cycles in the United States lead to medium-term fluctuations
            in Mexico; and why consumption is not less volatile than
            output in Mexico.
repnme: repnme: Medium-term business cycles in developing countries
display_title: Medium-term business cycles in
            developing countries
listing_relative_url: /research/2009/12/11445946/medium-term-business-cycles-developing-countries
topicv3: Innovation, Technology Transfer and
            Diffusion m1326019 1084,Manufacturing Sectors m1326521 1281,Energy and Extractives m1326595 507,Trade m1326924 698,Trade and FDI m1504264 2556
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 58
model_extractions: WPS5146 Policy Research Working Paper 5146 _Diego Comin Norman Loayza Farooq Pasha Luis Serven_ The World Bank Development Research Group Macroeconomics and Growth Team December 2009
Policy Research Working Paper 5146

# **Abstract**

Empirical evidence—including the current global crisis —suggests that shocks from advanced countries often have a disproportionate effect on developing economies. Can this account for the fact that aggregate fluctuations are larger and more persistent in the latter than in the former economies? And what are the mechanisms at play? This paper addresses these questions using a model of an industrial and a developing economy trading goods and assets, with (i) a product cycle shaping the range of intermediate goods used to produce new capital in each country, and (ii) investment adjustment costs in the developing economy. Innovation by the advanced economy results in new intermediate goods, at first produced at home, and eventually transferred to the developing economy through direct investment. The pace of innovation and technology transfer is driven by profitability. This process of technology diffusion creates a medium-term connection between both economies, over and above the short-term link through trade. Calibration of the model to match Mexico-United States trade and foreign direct investment flows shows that this mechanism can explain why shocks to the United States economy have a larger effect on Mexico than on the United States itself, and hence why Mexico shows higher volatility than the United States; why business cycles in the United States lead to medium-term fluctuations in Mexico; and why consumption is not less volatile than output in Mexico.

This paper—a product of the Macroeconomics and Growth Team, Development Research Group—is part of a larger effort in the department to understand the effects of innovation and technological upgrading on the macroeconomic performance of developing countries. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at nloayza@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 Research Support Team
# Medium-Term Business Cycles in Developing Countries<sup>1</sup>

Diego Cominy, Norman Loayzaz, Farooq Pasha� and Luis Servenz<sup>2</sup> Keywords: Business Cycles in Developing Countries, Co-movement between Developed and Developing economies, Volatility, Extensive Margin of Trade, Product Life Cycle, FDI. JEL Classification: E3, O3.

1For excellent research assistance, we are grateful to Freddy Rojas, Naotaka Sugawara, and Tomoko Wada. We have bene...tted from insightful comments from Susanto Basu, Antonio Fatás, Gita Gopinath, Aart Kraay, Marti Mestieri, Claudio Raddatz, Martin Ravallion, Julio Rotemberg, Lou Wells, and seminar participants at Harvard University, EIEF, and the World Bank. We gratefully recognize the ...nancial support from the Knowledge for Change Program of the World Bank. The views expressed in this paper are those of the authors, and do not necessarily re‡ect those of the institutions to which they are a¢ liated.

> 2yHarvard University and NBER, z The World Bank, � Boston College.
"Poor Mexico! So far away from God and so close to the United States." Attributed to Dictator Por...rio Diaz, 1910.

# 1 Introduction

At the end of 2007, the US economy entered a recession which, by the ...rst quarter of 2009, had reduced US GDP by 2.2%. The Mexican economy was showing no sign of distress until the US recession began. Despite that, Mexican GDP declined by 7.8% during the same period. This and similar episodes from other developing countries<sup>1</sup> motivate several questions: Why do shocks to developed economies a¤ect developing countries so much? Does the response of developing economies to shocks that originate in their developed neighbors account for the larger volatility of developing economies? More broadly, what ingredients do our models need to incorporate in order to account for the unique features of economic ‡uctuations in developing economies?

To investigate these questions, we build a two-country asymmetric DSGE model. One of the countries is developed (e.g., the US) while the other is a developing country (e.g., Mexico). The model has two salient features. First, a product cycle structure determines the range of intermediate goods used to produce new capital in each country. Second, we introduce investment ‡ow adjustment costs in the developing economy. On the product cycle, we follow the approach in Vernon (1966), Wells (1972), and Stokey (1991). New intermediate goods result from R&D expenditures in the US. To increase the range of intermediate goods exported to Mexico (i.e. extensive margin of trade), it is necessary to incur sunk costs. Further investments (i.e. FDI) can facilitate the transfer of the intermediate goods production to Mexico from where they are exported back to the US. On adjustment costs, we adopt the approach in Christiano, Eichenbaum and Evans (2005), where capital accumulation is subject to convex adjustment costs. These costs are incurred when the level of investment changes over time (so that they are zero in the steady state). Moreover, since adjustment costs are at least partially related to the quality of infrastructure and public services, we assume that they are primarily relevant in developing countries.

As in standard trade models, shocks to the US a¤ect the demand for Mexican exports. This generates a positive co-movement between the US and Mexico’s outputs in the short term.

> 1GDP decline over this period in the following sample of countries: Malaysia 7.8%, Philipines 12.1%, Singapore 7.4%, South Korea 3.3%, Taiwan 13.8%, Thailand 7.7%.

1
But this link is insu¢ cient to generate a larger and more persistent response in Mexico than in the US to a US shock that we see in the data. By making the extensive margin of trade and FDI endogenous, we introduce two mechanisms by which US shocks a¤ect the ‡ow of new technologies to Mexico. In particular, US shocks a¤ect the value of exporting and transferring technologies, inducing pro-cyclical investment in exporting new technologies and FDI ‡ows. Since on average the di¤usion of technology takes time, variations in the extensive margin of trade and FDI a¤ect Mexican productivity and output only gradually. This generates a hump-shaped response in these variables in response to a US shock.

Our model generates large ‡uctuations in Mexican productivity. This is at the root of why US shocks have larger and more persistent e¤ects on Mexican output than in the US itself. Intuitively, the slow pace of international di¤usion of intermediate goods generates a large gap between the stock of technologies available for production in the US and Mexico. As a result, when a shock a¤ects the return to exporting new technologies to Mexico, it induces very wide ‡uctuations in the ‡ow of new technologies exported to Mexico resulting in wide swings, over the medium term, in the stock of technologies in Mexico. In the US, in contrast, there is not such a large stock of technologies waiting to be adopted. Thus, the ‡uctuations in the stock of technologies and productivity are signi...cantly smaller than in Mexico.

Intermediate goods are used to produce new capital and the e¢ ciency of production of new capital is increasing in the number intermediate goods available in the economy. Thus, the reduction in the ‡ow of intermediate goods associated with a US recession generates a gradual increase in the price of Mexican capital. In the presence of adjustment costs, ...rms respond to the prospect of a higher future price of capital by reducing investment today. This decline in investment is the ultimate driver of the larger initial response of Mexican than US output to a US shock. The decline in the speed of di¤usion of intermediate goods to Mexico generates a subsequent decline in Mexican GDP.

Mexican shocks have a very small e¤ect on the US economy. However, they have important e¤ects on Mexican consumption, leading to what might be called excess sensitivity of consumption to output shocks. Even in our context of forward-looking equilibrium, this occurs because of the presence of both adjustment costs to investment and incomplete international credit markets for Mexico. The gradual increase in the price of capital that follows a recessionary shock in Mexico leads to higher real interest rates in Mexico despite the decline in the 2
marginal product of capital.<sup>2;3</sup> The prospect of higher current and future interest rates induces Mexican consumers to save, depressing consumption. The combination of adjustment costs and prospects of a higher future price of capital reduce the initial decline of investment and generate a counter-cyclical current account. This relaxes the resource constraint enabling a decline in Mexican consumption that is larger than the initial decline in output. As a result, the model is able to generate more volatile consumption than output in developing economies, which is a regularity documented in Aguiar and Gopinath (2007).

Section 4.3 presents evidence on the relevance of the key mechanisms in the model. First, it shows that the ‡ow of new intermediate goods to Mexico – measured by the growth in the number of six-digit manufacturing and durable manufacturing categories with positive US exports to Mexico –co-moves positively with both US and Mexican GDP. Second, the model predicts that this co-movement generates a strong lead of US output over Mexican GDP and over the relative price of capital in Mexico. We indeed ...nd that these predictions are borne by the data. Third, the model also predicts that one key aspect of the large e¤ect that US shocks have on Mexican GDP is the e¤ect that they have on Mexican investment. Consistent with this, we ...nd a strong positive co-movement between US GDP and Mexican investment in the data. Finally, a key driver of the high volatility of consumption in Mexico is the counter-cyclicality of the price of capital in Mexico which generates a similar cyclical pattern in interest rates. The data also support this mechanism since we ...nd that the relative price of capital is strongly counter-cyclical in Mexico and more so than in the US. It is important to remark that, in addition to matching these qualitative features of the data, our model provides a quantitatively accurate account of their strength.

Our model is related to several literatures. First, the empirical literature on synchronization of business cycle ‡uctuations across countries (e.g. Frankel and Rose 1997 and 1998) has shown that countries that trade more tend to have more synchronized business cycles.<sup>4</sup> Second, the literature on medium-term business cycles (Comin and Gertler, 2006, and Comin, Gertler and Santacreu, 2009) has shown that endogenous R&D and technology adoption mechanisms introduce signi...cant endogenous propagation and ampli...cation. This literature, however, has considered single-country models of developed economies and therefore is not suited to study

> 2In section 4 we provide evidence on the strong counter-cyclicality of the price of capital in Mexico.

> 3The counter-cyclicality of real interest rates in developing countries is emphasized by Neumeyer and Perri (2005).

> 4 More recently, Sosa (2008) has investigated the co-movement patterns of US and Mexico using VARs .

3
the co-movement between developed and developing countries.

Third, our model is related to Aguiar and Gopinath (2007), who argue that, in a reduced form sense, shocks to developing countries are more persistent than shocks to developed economies and use this to explain the higher volatility of consumption relative to output observed in developing countries. Our model provides a microfoundation for their assumption based on the slow di¤usion of technologies.

A fourth related literature uses small open economy macro models to explore business cycles in developing countries (e.g. Neumayer and Perri, 2005, Mendoza, 2008, and Tsyrennikov, 2007). This approach does not explicitly model the link between developed and developing economies. It instead assumes that domestic interest rates are linked to the world interest rates which are exogenous. As a result, they are not well suited to explain the observed leadlag relationship between Mexico and the US. Some of these models have been successful in generating a higher volatility in consumption than output with the introduction of frictions in capital markets. However, the type of capital ‡ows they rely on (international borrowing and lending) has become a small fraction of international capital ‡ows to developing countries. As shown by Loayza and Serven (2006), approximately 70% of the capital ‡ows to developing countries since 1990 have been FDI.<sup>5</sup> Our model takes the opposite approach of assuming that FDI is the only international capital ‡ow. In this sense, it is complementary to the SOE models.

Finally, our model is related to the new trade literature that has emphasized the relevance of the extensive margin of trade (i.e. how many intermediate goods are traded) to explain trade volumes (Melitz, 2003, Kehoe and Ruhl, 2002, and Bernard et al., 2007) and international comovement (Melitz and Ghironi, 2005, and Bergin, Feenstra, and Hanson, 2009).<sup>6</sup> The elegance and tractability of these models follows, in part, because the number of intermediate goods exported is not a state variable. This feature, however, makes di¢ cult for these models to generate the observed hump-shaped e¤ect of US shocks on Mexican output. The static nature of the extensive margin decision implies that it is basically driven by ‡uctuations in relative

> 5The FDI share is even larger when restricting attention to private capital ‡ows and when focusing in Latin America and Asia.

> 6This latter paper is the most complementary to ours. It develops an elegant model of outsourcing to explain the co-movement between the manufacturing sectors in the US and Mexico as well as the higher volatility in the Mexican manufacturing sectors than in the US. Co-movement follows from perfect international insurance of consumption and from the possibility of outsourcing production. The higher volatility follows from the smaller size of the outsourced sector in Mexico and because the cyclicality of US wages dampens the e¤ects of US demand shocks on domestic demand triggering outsourcing to Mexico.

4
wages. However, in the data, US wages have been almost acyclical over the last 20 years.<sup>7</sup> Hence, they are surely not the main source of co-movement between Mexico and the US. A ...nal di¤erence between our model and those of the new trade literature is that, since we have investment in physical capital, output and consumption in our model are quite di¤erent objects and we can attempt to understand why consumption is more volatile than output in developing countries.

The rest of the paper is organized as follows. Section 2 presents the model. Section 3 discusses the symmetric equilibrium and provides some intuition about the key mechanisms. Section 4 evaluates the model. Section 5 concludes.

# 2 Model

Before presenting the model, we brie‡y describe its main features. Ours is a two-country model with trade in intermediate goods. The number of intermediate goods available for production determines the technology to produce new capital. Three margins determine the number of intermediate goods available for production in each country: (i) R&D investments create new intermediate goods in the North (N ); (ii) investments in exporting intermediate goods enlarge the set of intermediate goods exported to the South (S); (iii) FDI transfers the production of the intermediate good to S: Capital markets are assumed to be perfect within countries but international capital ‡ows other than FDI are ruled out.

## 2.1 Resource constraints

Let Yct be gross ...nal output. In each country, ...nal output may be used for consumption, Cct, investment, Ict; paying overhead costs, Oct; and government spending, Gct. In addition, N<sup>0</sup> s output can be used to conduct research and development, St; that leads to new intermediate goods and to make intermediate goods suitable for export to S; Xt<sup>g: N 0s ...rms can also conduct</sup> foreign direct investment by using S<sup>0</sup> s ...nal output to transfer the production of the intermediate goods to S; Xt<sup>T.Theaggregateresourceconstraintscanthenbewrittenasfollows:</sup>

> 7The correlation between HP-...ltered output and real wages since 1990 in the US is 0.2.

5
In turn, let Jct be newly produced capital and �(:) be the depreciation rate of capital. Then capital evolve as follows: where gK denotes the steady state growth rate of capital. �(Uct) is the depreciation rate which is increasing and convex in the utilization rate as in Greenwood, Hercowitz and Hu¤man (1988). The convex function �c(:) represents the adjustment costs that are incurred when the level of investment changes over time. We assume that �c(1) = 0; �<sup>0</sup> c<sup>(1)=0;sothatthereareno</sup> adjustment costs in the steady state.<sup>8</sup> Note also that the function �c(:) is indexed by c re‡ecting international asymmetries in the magnitude of adjustment costs.

Next, let Pct<sup>kbe the price of this capital in units of domestic ...nal output.Given competitive</sup> production of ...nal capital goods, A distinguishing feature of our framework is that Pct<sup>kevolvesendogenouslyineachcountry.</sup> One of the key sources of variation in Pct<sup>kisthepaceatwhichnewtechnologiesembodiedin</sup> new intermediate goods arrive in the economy which depends on the agents response to overall macroeconomic conditions, as we describe below.

# 2.2 Capital

Physical capital is immobile across countries. It is produced in two stages. First, a continuum of Nct<sup>Kdi¤erentiated...rmsconstructnewcapital.EachusesasinputthecontinuumActofthe</sup> di¤erentiated intermediate capital goods available for production in the economy. Let Jct (r) be new capital produced by ...rm r and Ict<sup>r(s)the amount ofintermediate capitalthe ...rm employs</sup> from supplier s. Then with �> 1. Note that each supplier s of intermediate capital goods has a bit of market power. Pro...t maximization implies that the supplier sets the price of the s intermediate capital good 8This formulation is now standard in macro models (Christiano, Eichembaum and Evans (2005), Jaimovich and Rebelo (2008), and Comin, Gertler and Santacreu (2009)).

6
as a ...xed markup � times the marginal cost of production. In N; it takes one unit of ...nal output to produce one unit of intermediate. So, the marginal cost is unity. To capture the comparative advantage of the South in assembling manufacturing goods (e.g. Iyer, 2005), we assume that it takes 1=�(< 1) units of country S output to produce a unit of a intermediate good in S: In addition, there is an iceberg transport cost of shipping the good internationally. In particular, 1= (where < 1) units of the good need to be shipped so that one unit arrives.

Observe that there are e¢ ciency gains in producing new capital from increasing the number of intermediate inputs, Act. These e¢ ciency gains re‡ect embodied technological change and are the main source of variation in the relative price of capital, Pct<sup>k;overthelongandmedium</sup> term.

New capital, Jct, is a CES composite of the output of the Nct<sup>Kcapitalproducers,asfollows:</sup> with �<sup>K</sup> > 1.

We allow the number of capital producers Nct<sup>Ktobeendogenouslydeterminedbyafree</sup> entry condition in order to generate high frequency variation in the real price of capital that is consistent with the evidence (e.g. Comin and Gertler, 2006 and section 4.2 in this paper).<sup>9</sup> We ~~K~~ can decompose Pct<sup>Kintotheproductoftwoterms:themediumtermwholesaleprice,</sup> P ct<sup>;that</sup> is governed exclusively by technological conditions in the medium term and a high-frequency component, Pct<sup>K=P � K</sup> ct<sup>;thatisinsteadgovernedbycyclicalfactors.10</sup> We assume that the per period operating cost of a ...nal capital good producer, o<sup>k</sup> ct<sup>;grows</sup> with the medium term replacement value of the capital stock. Formally, where b<sup>k</sup> c<sup>isaconstant.AsinCominandGertler(2006),thiscapturesthenotionthatthe</sup> ~~k~~ operating costs are increasing in the sophistication of the economy, as measured by P ct<sup>Kct; and</sup>

> 9An alternative formulation with similar implications for the high frequency ‡uctuations in the relative price of capital would be to introduce counter-cyclical price markups.

> 10In particular,

7
guarantees balanced growth: At the margin, the pro...ts of capital producers must cover this operating cost. This arbitrage condition pins down Nct<sup>k:</sup>

## Optimal investment

The adjustment costs introduce a wedge between the price of new capital (Pct<sup>K) and the price</sup> of installed capital (Pct<sup>I)whenthe‡owofrealinvestmentdeviatesfromthesteadystatelevel.</sup> As a result, ...rms will tend to smooth out investment ‡ows. Formally, the wedge is given by the following condition where

# 2.3 Technology

The e¢ ciency of the production of new capital goods depends on the number of intermediate goods available for production Act: Next, we describe the processes of invention, international di¤usion and transfer of production which is inspired by the product lifecycle literature (Vernon, 1966). Intermediate goods are invented in country N and at this ...rst stage they are local (i.e. can only be used in N ): After successfully undertaking a stochastic investment, the good becomes global (i.e. can be exported to S): At a ...nal stage, the production of intermediate goods can be transferred to S in order to bene...t from the comparative advantage of S at producing intermediate goods. This entails another stochastic investment though this time it is in terms of country S output. These investments constitute the ‡ow of FDI from N to S: We denote by A<sup>l</sup> ; A<sup>g</sup> and A<sup>T</sup> the stock of local, global and transferred intermediate goods: The total number of intermediate goods available in each country is therefore given by 8
Technology ‡ows determine trade ‡ows. Country N exports to S the A<sup>g</sup> intermediate goods which have become exportable while S exports to N the A<sup>T</sup> intermediate goods whose production has been transferred to S: The only other good that is traded in this economy is energy as we discuss below. Next we present the conditions that characterize the technology dynamics in each economy.

# Creation of new intermediate goods

Innovators in N create new intermediate goods by investing ...nal output into R&D activities. In exchange they are granted a patent which ensures the monopolistic rents from being the sole producer of the intermediate good. R&D is ...nanced with loans from the households. Let St(p) be the total amount of R&D by innovator p: Let 't be a productivity parameter that the innovator takes as given and let 1 ¬ � the probability that any existing intermediate good becomes obsolete in the subsequent period. Then, the law of motion for the stock of technologies developed by innovator p is: We assume that 't depends on the aggregate stock of innovations in N , ANt, the medium ~~k~~ term wholesale value of the capital stock P Nt<sup>KNt;andaggregateresearchanddevelopment</sup> expenses St as follows: with 0 < � � 1 and where � is a scale parameter. This formulation is borrowed from Comin and Gertler (2006) and permits us ‡exibility in calibrating the impact of R&D while ensuring the existence of a balanced growth path without scale e¤ects.

In equilibrium, agents engage in R&D activities until the cost of developing a new intermediate good (LHS) equalizes its expected market value (RHS).

where vt is the market value of the patent to produce a local intermediate good. vt can be de...ned by the following Bellman equation where �t denotes the per period pro...ts of a local intermediate goods producer, x<sup>g</sup> t<sup>is the number</sup> of units of ...nal output spent in adapting the intermediate good for use in country S, �(�t<sup>gxg</sup> t<sup>)</sup> 9
is the associated probability of a successful adaptation where �(:) satis...es �<sup>0</sup> > 0; �<sup>00</sup> < 0, v<sup>g</sup> is the market value of a global intermediate good; and �<sup>g</sup> t<sup>isascalingfactor,takenasexogenous</sup> by the innovator, which adjusts slowly over time, and ensures balanced growth, and is equal to where b<sup>g</sup> is a positive constant.

# Investment in exporting

Intermediate goods producers in N can expand the market for their products by exporting them to S: Prior to this, however, the producer must successfully market the intermediate good in S and adapt it to be suitable for production in S: The optimal intensity of this investment equalizes at the margin the cost and the expected bene...ts of exporting the intermediate good to S as shown in the following ...rst order condition: The marginal cost of investing one unit of output in exporting the good (LHS) is 1, while the expected marginal bene...t is equal to the associated increase in the probability of exporting times the discounted gain from transforming the local good in a global intermediate good.

In the symmetric equilibrium, all producers of local intermediate goods invest the same amount in making the good exportable to S; and, as a result, face the rate of transformation of local into global intermediate goods, �<sup>g</sup> t<sup>:ThelawofmotionforAgis</sup> After expanding the market to S; the value of an intermediate good, vt<sup>g;isgivenby</sup> where �<sup>g</sup> t<sup>denotes the per period pro...ts of a global intermediate goods producer, xT</sup> t<sup>is the num-</sup> ber of units of country S<sup>0</sup> s ...nal output spent by the innovator in transferring the production of the intermediate good to S; et is the exchange rate (dollars per peso), �(�<sup>T</sup> t<sup>xT</sup> t<sup>) is the associated</sup> probability of successfully completing this foreign direct investment, where the function �(:) satis...es �<sup>0</sup> > 0; �<sup>00</sup> < 0, v<sup>T</sup> is the market value of the company that produces a transferred 10
intermediate good; and �<sup>T</sup> t<sup>isascalingfactor,takenasexogenousbytheinnovatorandequal</sup> to where b<sup>T</sup> is a positive constant.

## Foreign direct investment

Let �<sup>T</sup> t<sup>betherateatwhichtheproductionofglobalintermediategoodsistransferredfrom</sup> N to S: The law of motion for the stock of transferred intermediate goods, A<sup>T</sup> t<sup>;canbewritten</sup> as follows: The optimal intensity of FDI, x<sup>T</sup> t<sup>; equalizes the private marginal costs and expected bene...ts</sup> of transferring the production to S: The marginal cost is et, while the expected marginal bene...t is the increase in the probability of succeeding in the FDI times the discounted gain from transferring the production of the intermediate good to S.

Finally, the market value of an intermediate good whose production has been transferred to S is given by where �<sup>T</sup> t<sup>denotestheperperiodoperatingglobalpro...tsofthecompanythatproducesa</sup> transferred intermediate good.

# 2.4 Production of gross output

Gross output, Yct; is produced in two stages. At the ...rst stage, each of Nct di¤erentiated output producers, indexed by j, combine capital, Kcjt, labor, Lcjt, and energy, Ecjt, to produce its di¤erentiated output, Yct(j) according to the following Cobb-Douglas technology: where g is the exogenous growth rate of disembodied productivity,<sup>11</sup> and U denotes the intensity of utilization of capital. The markets where ...rms rent the factors of production (i.e. labor and

> 11For simplicity, we assume that it is exogenous. It is quite straightforward to endogenize it as shown in Comin and Gertler (2006).

11
capital) are perfectly competitive.

At the second stage, gross output, Yct; is produced competitively by aggregating the Nct di¤erentiated ...nal goods as follows: where �(> 1) is inversely related to the price elasticity of substitution across goods. Producers of di¤erentiated output must pay every period an overhead cost, oct; given by Free entry equalizes the per period operating pro...ts to the overhead costs determining the number of ...nal goods ...rms Nct.

# 2.5 Energy endowments

Oil represents a signi...cant share of Mexican exports to the US. To account for this in the calibration of the model, we assume that the government in country S is endowed with ESt<sup>e</sup> units of energy. Let Ect denote the aggregate consumption of energy in country c. Country N imports Et<sup>xunitsofenergytocountryS;andbuystherestofitsenergyneeds,E</sup> t<sup>w,fromthe</sup> rest of the world. The energy consumption in each country satis...es the following identities: For simplicity, we assume that the price of energy, P<sup>E</sup> , is ...xed.

# 2.6 Households

There is a representative household that consumes, supplies labor and saves. It may save by either accumulating capital or lending to innovators. The household also has equity claims in all monopolistically competitive ...rms. It makes one period loans to innovators and also rents capital that it has accumulated directly to ...rms. It is important to stress, though, that there is no international lending and borrowing. That is, US FDI in Mexico is the only item in the Mexican ...nancial account.

12
Let Cct be consumption and �<sup>w</sup> ct<sup>apreferenceshifter.Thenthehouseholdmaximizesits</sup> present discounted utility as given by the following expression: subject to the budget constraint where �ct re‡ects the pro...ts of monopolistic competitors paid out fully as dividends to households, Dct denotes the rental rate of capital, Bct is the total loans the household makes at t ¬ 1 that are payable at t; and Tct re‡ects lump sum taxes.

## Government

Government spending is ...nanced every period with lump sum transfers and the revenues from energy:

# 3 Symmetric equilibrium

We defer to the Appendix the formal de...nition and complete characterization of the equilibrium. Here we just present the main equations to highlight the e¤ects of endogenizing the investment decisions that determine the extensive margin of trade and FDI. In a model without these investments, such as Comin and Gertler (2006), capital, Kct; and the stock of intermediate goods, ANt; are the only endogenous state variables. Here, we have two additional endogenous states, the stock of global intermediate goods, A<sup>g</sup> t<sup>;andthestockoftransferredintermediate</sup> goods, A<sup>T</sup> t<sup>whichintroducenewdynamicsinMexicanoutputandtherelativepriceofcapital.</sup> The relevant equations of motion are thus given by (3), (19), (22) and It is convenient to de...ne the variable aNt as the ratio of the e¤ective number of intermediate good in N relative to A<sup>l</sup> t<sup>;andaStastheratioofthee¤ectivenumberofintermediategoodsin</sup> 13
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lower demand for S<sup>0</sup> s exports but also generates a more persistent decline driven by the lower productivity.

Since intermediate goods are the source of embodied technical change, the slow response of ASt to shocks generates counter-cyclical ‡uctuations in the Mexican price of capital over the medium term. introduces important dynamics in the Mexican relative price of capital (39).<sup>13</sup> Mexican ...rms would like to reduce drastically investment precisely when the price of new capital peaks. However, this would be too costly because of the costs of adjusting the ‡ow of investment. Instead, in anticipation of the future higher price of capital, ...rms start reducing investment when the contractionary shock hits the US economy. This collapse in investment adds to the lower demand for Mexican exports generating a larger initial e¤ect of US shocks in Mexican than in US output. As we shall see, this explains why developing economies are more volatile than their developed neighbors.

In the neoclassical growth model, the interest rate is equal to the marginal product of capital net of depreciation. Since the marginal product of capital is pro-cyclical, so are interest rates. However, Neumeyer and Perri (2005) show that in developing countries interest rates are counter-cyclical. This is the case also in our model because, in addition to the marginal product of capital, interest rates also depend on the increment in the price of installed capital.

Recall from the optimal investment equation (10) that the price of installed capital is equal to the price of new capital plus a wedge that re‡ects changes in investment ‡ows. Thus, the prospects of increases in the price of new capital in response to a contractionary shock, lead to high interest rates today. This e¤ect adds to the standard permanent income e¤ect of output on consumption generating a very signi...cant contraction in consumption in S.

The adjustment costs contribute to making the decline in consumption feasible. In particular, they moderate the initial collapse in Mexican investment following a recessionary domestic

> 13Short term ‡uctuations in the relative price of capital are driven by the exchange rate and by pro-cyclical entry.

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shock absorbing resources that force Mexican consumption to decline. As we shall see below, these mechanisms can explain why consumption is not less volatile than output in developing countries.

# 4 Model Evaluation

In this section we explore the ability of the model to generate cycles at short and medium term frequencies that resemble those observed in the data in developed and, specially, in developing economies. Given our interest in medium term ‡uctuations, a period in the model is set to a year. We solve the model by loglinearizing around the deterministic balanced growth path and then employing the Anderson-Moore code, which provides numerical solutions for general ...rst order systems of di¤erence equations. We describe the calibration before turning to some numerical exercises.

## 4.1 Calibration

The calibration we present here is meant as a benchmark. We have found that our results are robust to reasonable variations around this benchmark. To the extent possible, we use the restrictions of balanced growth to pin down parameter values. Otherwise, we look for evidence elsewhere in the literature. There are a total of twenty-six parameters. Twelve appear routinely in other studies. Six relate to the process of innovation and research and development and were introduced in Comin and Gertler (2006). Finally, there are six new parameters that relate to trade and the process of international di¤usion of intermediate goods and two related to the adjustment costs. We defer the discussion of the calibration of the standard and R&D parameters to the Appendix and focus here on the adjustment costs parameters and those that govern the interactions between N and S: We treat asymmetrically adjustment costs in Mexico and the US. We do this for two reasons. First, there is ample evidence on the larger costs of entry, obtaining construction permits and import licenses in Mexico relative to the US (e.g. Gwartney et al., 2007, World Bank, and Miller and Holmes, 2009). Second, above and beyond the micro evidence on adjustment costs, our goal is to build a model of the Mexican economy and its response to US shocks. To achieve this goal, we need to build a model of the US economy that resembles as much as possible the data. As we discuss below, even when we set �<sup>00</sup> N<sup>(1)tozero,ourmodelgeneratesseriesfor</sup> 16
US investment that have less volatility than in the data. Introducing adjustment costs to US investment would accentuate this problem.

There are no estimates, to the best of our knowledge, for �<sup>00</sup> S<sup>:Giventhat,wethinkthata</sup> conservative estimate is a value in the upper end of the range of estimates for the adjustment cost parameter in the US. We use the estimate of Christiano, Eichenbaum and Evans (2005) and set �<sup>00</sup> S<sup>(1)to1.5.Wealsoset�00</sup> N<sup>(1)to0:</sup> We calibrate the six parameters that govern the interactions between N and S by matching information on trade ‡ows, and US FDI in Mexico and micro evidence on the cost of exporting and the relative productivity of US and Mexico in manufacturing. First, we set � to 2 to match the Mexican relative cost advantage over the US in manufacturing identi...ed by Iyer (2005). We set the inverse of the iceberg transport cost parameter, ; to 0.95,<sup>14</sup> the steady state probability of exporting an intermediate good, �<sup>g</sup> ; to 0.0875, and the steady state probability of transferring the production of an intermediate good to S; �<sup>T</sup> ; to 0.0055 to approximately match the share in Mexican GDP of Mexican exports and imports to and from the US (i.e. 18% and 14%, respectively) and the share of intermediate goods produced in the US that are exported to Mexico. Speci...cally, Bernard, Jensen, Redding and Schott (2007) estimate that approximately 20 percent of US durable manufacturing plants export. However, these plants produce a much larger share of products than non-exporters. As a result, the share of intermediate goods exported should also be signi...cantly larger. We target a value of 33% for the share of intermediate goods produced in the US that are exported. This yields an average di¤usion lag to Mexico of 11 years which seems reasonable.

Das, Roberts and Tybout (2006) have estimated that the sunk cost of exporting for Colombian manufacturing plants represents between 20 and 40 percent of their annual revenues from exporting. We set the elasticity of �<sup>g</sup> with respect to investments in exporting, �g; to 0.85 so that the sunk cost of exporting represents approximately 30 percent of the revenues from exporting. The elasticity of �<sup>T</sup> with respect to FDI expenses, �T ; together with the steady state value of �<sup>T</sup> determine the share of US FDI in Mexico in steady state. We set �T to 0.5 so that the US FDI in Mexico represents approximately 2% of Mexican GDP.

> 14Interestingly, the value of required to match the trade ‡ows between the US and Mexico is smaller than the values used in the literature (i.e. 1/1.2 in Corsetti et al., 2008) because of the closeness of Mexico and the US and their lower (inexistent after 1994) trade barriers.

17
# 4.2 Impulse response functions

To be clear, the exercises that follow are meant simply as a ...rst pass at exploring whether the mechanisms we emphasize have potential for explaining the data: They are not formal statistical tests. For simplicity, the only two shocks we consider are innovations to the wage markup, �<sup>w</sup> ct<sup>,inN(US)andinS(Mexico):Severalauthors15havearguedthattheseshocks</sup> may capture important drivers of business cycles. However, we are not vested in the nature of the shocks. We show that the our conclusions are robust to other shocks (i.e. productivity and relative price of capital).

## Response to a US shock

Figure 1 displays the impulse response functions to a US wage markup shock. Solid lines are used for the responses in Mexico while dashed lines represent the responses in the US. The response of the US economy to a domestic shock is very similar to the single-country version presented in Comin and Gertler (2006). In particular, a positive wage markup shock contracts the US labor supply (panel 2) causing a recession in the US (panel 1). In addition to the decline in hours worked, the initial decline in US output is driven by exit in the ...nal goods sector and by a decline in the utilization rate. The response of US output to the shock is more persistent than the shock itself (panel 12) due to the endogenous propagation mechanisms of the model. In particular, the domestic recession reduces the demand for intermediate goods and, hence, the return to R&D investments. This leads to a temporary decline in the rate of development of new technologies but to a permanent e¤ect on the level of new technologies relative to trend. The long run e¤ect of the shock on output is approximately 45% of its initial response.

The US shock has important e¤ects on the Mexican economy. Upon impact, the shock causes a decline in Mexican output that is larger than the US contraction (0.63 vs. 0.46). The Mexican recession is driven by two forces: the decline in the demand for Mexican exports to the US (panel 10) and the collapse of Mexican investment (panel 4).

Unlike the US, the response of Mexican output to a US shock is hump-shaped. At the root of this response we ...nd the dynamics of international technology di¤usion. In particular, the shock to �<sup>w</sup> Nt<sup>reducesthereturnonexportingnewintermediategoodsandtransferringtheir</sup> production to Mexico. As a result, fewer resources are devoted to these investments (panel 7) gradually reducing the stock of intermediate goods in Mexico relative to the steady state (panel 8). Since productivity is determined by the stock of intermediate goods, the slow international

> 15E.g. Hall (1997 ), Gali, Gertler and Lopez-Salido (2002).

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di¤usion of new technologies also leads to a gradual decline in Mexican productivity which causes a hump-shaped response of output.<sup>16</sup> Our model generates large ‡uctuations in Mexican productivity. This is at the root of why US shocks have larger e¤ects on Mexican output than in the US itself. Intuitively, the slow pace of international di¤usion of intermediate goods generates a large gap between the stock of technologies available for production in the US and Mexico. As a result, when a shock a¤ects the return to exporting new technologies to Mexico, it induces very wide ‡uctuations in the ‡ow of new technologies exported to Mexico resulting in wide swims, over the medium term, in the stock of technologies in Mexico. In the US, in contrast, there is no such a large stock of technologies waiting to be adopted. Thus, the ‡uctuations in the stock of technologies and productivity are signi...cantly smaller than in Mexico.

To illustrate further the role of the international di¤usion of technologies in the Mexican output dynamics, Figure 2 plots the impulse response function to a shock to �<sup>w</sup> Nt<sup>after shutting</sup> down the extensive margin of trade and FDI channels. When eliminating these linkages between the US and Mexico, the e¤ect of the shock on Mexican output is (i) always smaller than in the US, (ii) monotonic and (iii) signi...cantly less persistent than when these adoption margins are endogenous.

In contrast, in our model, the response of Mexican output to a US shock is more persistent than the US response and much more persistent than the shock itself. Thus, endogenous international technology di¤usion can provide a microfoundation for the ...nding of Aguiar and Gopinath (2007) that (in a reduced form speci...cation) the shocks faced by developing countries are more persistent than those faced by developed economies.

The gradual decline in ASt slowly reduces the e¢ ciency of production of new capital leading to a gradual increase in the price of capital (panel 6). The initial response of Mexican investment to these prospects for the price of capital largely depends on the magnitude of the adjustment costs. Figure 3 reports the impulse response functions to a contractionary �<sup>w</sup> Nt<sup>shockwith</sup> no adjustment costs. In the absence of adjustment costs, ...rms want to time the decline in investment with the peak in the price of new capital. As a result investment does not decline initially but declines sharply later on.

In the presence of adjustment costs, it is very costly to follow this strategy and companies start reducing their investment when the shock hits the economy in anticipation of the future

> 16In the US the response to the shock is monotonic because of the larger e¤ect of the shock on domestic demand and because technology di¤uses faster domestically than internationally.

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increase in the price of capital. As a result, a contractionary US shock generates a collapse of Mexican investment upon impact (panel 4 of Figure 1) which continues to decline as the price of capital increases and the economy contracts further. As we shall show below, the data supports the model’s prediction of a strong co-movement between US output and Mexican investment.

The response of investment to US shocks signi...cantly ampli...es the initial response of Mexican output to the US shock. To see this, compare the output responses with and without adjustment costs (i.e. Figure 1 vs 3). In the absence of adjustment costs, Mexican investment does not decline when the shock hits the economy and the only force that drives the Mexican recession is the decline in demand for Mexican exports to the US. Since the share of exports in Mexican GDP is not that large, Mexican output declines only by 0.05% in response to a 1% increase in �<sup>w</sup> Nt<sup>:Withadjustmentcosts,thecollapseofinvestmentcontributestotheMexican</sup> recession and output declines by 0.66% in response to the same shock. Note however, that in both cases, the decline in Mexican output eventually exceeds the size of the recession generated in the US. Similarly, the hump-shaped response of Mexican output is independent of the calibration of the adjustment costs.

For concreteness, we have used wage markup shocks as the sole source of ‡uctuations in our model. It is important to stress that our ...ndings do not hinge on the nature of the shock. This is illustrated in Figure 4 where we consider the model’s response to other two shocks that play a signi...cant role in the business cycle literature. These are a (negative) TFP shock (second row) and to a (positive) shock to the price of investment (third row).<sup>17</sup> In response to these shocks, the model also generates a large initial decline in Mexican output driven partly by a collapse in investment and a subsequent contraction in productivity due to a decline in the ‡ow of technologies to Mexico.

# Response to a Mexican shock

Figure 5 displays the impulse response functions to a Mexican wage markup, �<sup>w</sup> St<sup>;shockin</sup> the US (dashed) and in Mexico (solid). There are some striking di¤erences with Figure 1. First, a Mexican shock has virtually no e¤ect in the US. This follows from the di¤erence in size between the two economies but also from the fact that technologies ‡ow from the US to Mexico and not otherwise. One consequence of this is that the Mexican shock has a smaller e¤ect than the US shock on the extensive margin of trade and FDI. As a result, the e¤ect of �<sup>w</sup> St<sup>onMexicanGDPismoretransitorythanthee¤ectofaUSshock.</sup> However, the most signi...cant observation from Figure 5 is that Mexican shocks have a larger

> 17Figure A.1 in the appendix, shows the equivalent responses for the model without adjustment costs.

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e¤ect on Mexican consumption than on output. This is the result of both the endogenous relative price of capital and the adjustment costs. We explain next the intuition for this result.

By the logic explained above, a contractionary shock leads to a gradual increase in the price of capital. The prospect of a future higher price of capital has two e¤ects. On the one hand, it prevents investment from falling too much initially. (This is also achieved by the adjustment costs. See the contrast with the impulse response to a Mexican shock in the model without adjustment costs in Figure 6.)<sup>18</sup> On the other, they raise current and future interest rates despite the lower marginal product of capital due to the recession. Current and future high interest rates induce consumers to save more today hence reducing their consumption.

Such a signi...cant decline in Mexican consumption is feasible for two reasons. First, investment does not fall too much initially. Second, consistent with the data, the trade balance is very counter-cyclical. This, in turn, is a consequence of the persistent response of investment to the shock. Because the response of Mexican investment is so persistent, the value of transferring the production of intermediate goods to Mexico, v<sup>T</sup> ; declines more than net income from transferred technologies, �<sup>T</sup> ; (panel 9). This leads to a very signi...cant decline in FDI in‡ows into Mexico. (A phenomenon that the “sudden stops”literature (e.g. Calvo 1998) has tried to explain.) To reestablish the international equilibrium, the peso depreciates leading to a trade surplus that absorbs resources, forcing Mexican consumption to fall.<sup>19</sup> Note that one of the key drivers of the high volatility of consumption in Mexico is the counter-cyclicality of the price of capital. This important prediction is borne by the data. The price of new capital<sup>20</sup> in Mexico is very counter-cyclical at the high frequency with a correlation between HP-...ltered output and HP-...ltered price of capital of -0.55.<sup>21</sup> Interestingly, the price of new capital is signi...cantly more counter-cyclical in Mexico than in the US where the equivalent correlation is -0.08.<sup>22</sup> This may explain why consumption is as volatile as GDP in Mexico but

> 18Adjustment costs smooth the initial response of Mexican investment to the domestic shock. This has two e¤ects. On the one hand, it absorbs resources forcing consumption to decline. On the other, it increases the persistence of the e¤ects of the shocks, amplifying the decline in capital gains from exporting and conducting FDI to Mexico. As a result, the price of capital in Mexico ‡uctuates more genarating a larger appreciation in the Mexican price of capital which leads to higher interest rates in response to the shock.

> 19The strong counter-cyclical current account is documented by Neumeyer and Perri (2005) in a sample of developing countries (which includes Mexico).

> 20This is measured by the investment de‡ator over the GDP de‡ator.

> 21The counter-cyclicality of the price of new capital in Mexico is robust to other ...ltering methods. For example, the correlation between the growth rate in the price of capital and HP-...ltered output is -0.65.

> 22Over the medium term cycle the correlation between the Mexican price of capital and GDP is -0.71. In

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not in the US.

Comparing Figures 1 and 5, it is clear that the high relative volatility of consumption in Mexico is driven by Mexican shocks rather than by US shocks. This is the case because Mexican shocks have a much larger e¤ect on Mexican interest rates than US shocks. Intuitively, US shocks trigger a more persistent decline in Mexican output than Mexican shocks. As a result, Mexican companies want to cut their investment more drastically in response to them. This leads to a larger initial increase in the price of installed capital (PS<sup>I) which reduces the increase</sup> in the slope of PS<sup>Iduetothegradualincreaseinthepriceofnewcapital(P K</sup> S<sup>).23Hence,the</sup> lower increase in interest rates following a recessionary shock in the US vs. Mexico.

Before moving on to the quantitative analysis of the model it is worthwhile making a remark about the relative volatility of consumption and output in the US. Note that, according to Figure 3, consumption is more volatile than output in the model. This is a counter-factual prediction that follows from the assumption that the US only trades with Mexico. This assumption implies that the price of capital in the US increases very gradually in response to a decline in FDI to Mexico. (Recall that transferring the production of intermediate goods reduces their price in the US.) As argued above, the prospect of a higher future price of capital in the US reduces the decline in current investment and increases current and future interest rates leading to a larger decline in US consumption.

In reality, the US imports a large share of its intermediate goods from many countries in addition to Mexico including many developed economies that do not obtain their intermediate goods only from the US. As a result, the actual number of intermediate goods imported by the US is more independent from US shocks than in the model and the price of capital in the US increases less gradually than in Figure 3. This intuition is illustrated in Figure A2 were we present the impulse responses (to the three types of shocks) of the version of the model without the international di¤usion of intermediate goods. In this extreme case where US shocks do not a¤ect the technology available for production in other countries, the initial response of investment is much more pronounced than in Figure 3 and the response of the US price of capital is less gradual. This results in a consumption process that is less volatile than US the US, the correlation between these variables over the medium term is -0.55. For the full post-war period the correlations in the US are slightly larger (in absolute value). -0.18 for HP-...ltered data and -0.66 over the medium term.

> 23A decline in investment leads to an increase in the price of installed capital because the adjustment costs embedded in (3) imply that lower levels of investment today increase the costs of investment tomorrow.

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output.<sup>24</sup> Next, we look at the Mexican post-1990 data as a case study to evaluate the predictions of our model.

# 4.3 Mexico 1990-2007<sup>25</sup>

As in many other developing economies,<sup>26</sup> Mexican output is more volatile than that of the US. Table 1 reports the standard deviation of GDP per working age person<sup>27</sup> at the business cycle (or high) frequency (...rst column) and over the medium term cycle (third column) for the US (row 10) and Mexico (row 1).<sup>28</sup> Mexico’s output ‡uctuations at high and medium term frequencies are approximately twice more volatile than those of the US.

Our model predicts that an important factor contributing to the higher volatility of the Mexican economy is that Mexican GDP responds signi...cantly to US shocks while the US does not respond much to Mexican shocks. To explore these predictions Figure 7A plots US and Mexican GDP ...ltered using an HP ...lter to capture the high frequency (i.e. business cycle) ‡uctuations. The correlation coe¢ cient between the two is 0.43 and, despite the short length of the series, it is signi...cant at the 10% level. Beyond this statistic, the internet-driven expansion in the US during the second half of the 90s was accompanied by a similar expansion in Mexico. The 2001 US recession driven by the burst of the dot-com bubble also coincided with a decline in Mexican GDP that quickly recovered following the US expansion between 2002 and 2007. Finally, the US ...nancial crisis of 2008 also had a strong impact in Mexican GDP though this

> 24This is also the case in the single-country model of Comin and Gertler (2006) where the volatility of consumption and output match the US data.

> 25We restrict our attention to the post 1990 period for two reasons. First, the volume of US-Mexico trade and FDI increased very signi...cantly during this period making the mechanisms emphasized by our model much more relevant than before. Second, after 1990 FDI became the most signi...cant source of capital ‡ows from developed to developing economies making the model’s assumptions about the capital markets most appropriate for this period.

> 26See, for example, Neumeyer and Perri (2005).

> 27In what follows we scale all variables by working age population, i.e. population aged between 16 and 64.

> 28To be precise, we follow the de...nitions of medium term used by Comin and Gertler (2006). In particular, the sort run or high frequency will be measured using an HP ...lter which roughly isolates frequencies associates with cycles of amplitude smaller than 8 years. The medium term refers to frequencies associated with cycles of amplitude between 8 and 50 years. The medium term cycle is the “sum”of the high frequency and the medium term. That is, it captures cycles with amplitude smaller than 50 years. Comin and Gertler (2006) show that despite the relatively short time series, medium term cycles can be identi...ed in the data quite precisely.

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did not show yet in 2008 average annual output.<sup>29</sup> It seems reasonable to argue that none of these shocks had a direct e¤ect on the Mexican economy and, therefore, the co-movement with US GDP resulted from the international transmission of US ‡uctuations. The only important Mexican shock over this period was the 1995 recession which, despite its virulence, was relatively short-lived and had no e¤ect on the US. These observations are consistent with our model predictions that domestic shocks to S have less persistent consequences in S than shocks to N; and have virtually no e¤ect on N: The model also predicts that US shocks should have an e¤ect on medium term ‡uctuations in Mexico and that this e¤ect should be strongest with a lag. The ...rst row of Table 3 reports the correlation between HP-...ltered US GDP at various lags and the medium term component of Mexican GDP. Speci...cally, the contemporaneous correlation is 0.28 and increases to 0.49 after a year and to 0.53 after two. Despite the short length of the series, the lagged correlation coe¢ cients are signi...cantly di¤erent from 0 at conventional levels.

To obtain a better understanding of the data that underlies this co-movement pattern, Figure 7B plots the medium term component of Mexican GDP together with HP-...ltered US GDP. The lead-lag relationship between these variables can be most notably seen during the post 1995 expansion, the 2001 recession and the post 2001 expansion. Despite the severity of the e¤ect of the Tequila crisis on the medium term component of Mexican GDP, the latter strongly recovered with the US post-1995 expansion. The Mexican recovery lagged the US boom by about two years. The end of the Mexican expansion also lagged the end of the US expansion by one year. Finally, the post-2001 US expansion also coincided with a boom in the medium term component of Mexican GDP.

In contrast, the cross-correlogram between HP-...ltered Mexican GDP and the medium term component of Mexican GDP (row 3) monotonically declines after the maximum correlation that occurs contemporaneously.<sup>30</sup> To conclude this brief case study, we explore whether the margins that generate the comovement in our model are also pro-cyclical in the data. Table 2 shows that bilateral trade ‡ows between the US and Mexico are pro-cyclical. The table also reports the cyclicality of

> 29Between 2007:IV and 2008:IV Mexican real GDP declined by 1.75%. In contrast, annual GDP increased by 1.4% between 2007 and 2008.

> 30Figures A3 and A4 show similar co-movement patterns when using VAR methods to identify high frequency innovations to US and Mexican GDP. Speci...cally, we identify US shocks and Mexican shocks by running bivariate VARs under the identi...cation restriction that innovations to US GDP may a¤ect Mexico contemporaneously but innovations to Mexican GDP (or any other Mexican variable) do not a¤ect the US contemporaneously.

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two measures of the increment in the number of intermediate goods exported from the US to Mexico. Namely, the growth rate of the number of 6-digit classi...cation codes in manufacturing and in durable manufacturing in which the volume of exports from the US to Mexico is larger than $1 million in a given year. These measures of the extensive margin of trade vary also pro-cyclically with both US and Mexican GDPs. Finally, Table 2 reports a positive (though insigni...cant) co-movement between US FDI to Mexico (as a share of Mexican GDP) and both US and Mexican GDP. Reassuringly, this co-movement becomes statistically signi...cant when we remove some noise from the FDI series by ...ltering it to keep the medium term ‡uctuations.

# 4.4 Simulations

After showing that, qualitatively, our model is consistent with the main patterns in the data we next explore its ability to account for them quantitatively. To this end, we calibrate the volatility and persistence of wage markups shocks in the US and Mexico and run 1000 simulations over a 17-year long horizon each. Speci...cally, we impose the same autocorrelation for the wage markups in both Mexico and the US (0.6 annually) to re‡ect our view that much of the di¤erence in the persistence of the “reduced form” shocks that hit the two economies arises from the endogenous international di¤usion of technologies.<sup>31</sup> We calibrate the volatility of the shocks by forcing the model to match the high frequency standard deviation of GDP in Mexico and the US. This yields a volatility of the wage markup shock of 3.76% in the US and 4.97% in Mexico. Note that this signi...cantly higher volatility of the Mexican shock is consistent with the view that developing economies su¤er larger shocks than developed neighbors. Below we explore whether the higher volatility of the shocks is a signi...cant factor in explaining the higher GDP volatility in developing economies.

## Volatility

Table 1 compares the standard deviations of the high frequency and medium term cycle ‡uctuations in the data and in the model. Our calibration strategy forces the model to match the volatilities of output in Mexico and the US at the high frequency. In addition, the model

> 31We borrow this value from Comin and Gertler (2006) that estimate that this is the required autocorrelation to match the persistence of the US total markup (i.e. the sum of the price and wage markup). Note that, because of the propagation obtained from the endogenous technology mechanisms, this class of models require a smaller autocorrelation of the shocks to match the persistence in macro variables. In short, they are not a¤ected by the Cogley and Nason (1995) criticism that the Neoclassical growth model does not propagate exogenous disturbances.

25
also matches the observed volatility of output over the medium term both in Mexico (0.038 vs. 0.037 in the data) and in the US (0.02 vs. 0.015 in the data). Note that there is nothing in our calibration strategy that forces the model to matching the variance of output at lower frequencies. Matching these moments implies that the model induces the right amount of propagation of high frequency shocks into the medium term.

The model does a good job in reproducing the volatility observed in the data in variables other than output. It does a remarkable job in matching the volatility of consumption in Mexico both at the high frequency (0.03 vs. 0.031 in the data) and over the medium term cycle (0.038 vs. 0.04 in the data). This is of special interest given the attention that the international macro literature has given to these moments.

It also generates series for investment, the relative price of capital, bilateral trade ‡ows, the extensive margin of trade and FDI ‡ows that on average have similar volatilities to those observed in the data. For those instances where there is some di¤erences, the empirical volatilities fall within the 95% con...dence interval for the standard deviation of the simulated series.<sup>32</sup>

# Co-movement

Table 2 reports the contemporaneous correlation between the HP-...ltered Mexican variables and HP-...ltered output in both Mexico and the US. Broadly speaking, the model does a very good job in capturing the contemporaneous co-movement patterns both within Mexico but also between Mexico and the US. First, the model generates the strong co-movement between US and Mexican GDPs observed in the data. Speci...cally, the average correlation between these variables in our simulations is 0.71 with a con...dence interval of (0.4 , 0.9) that contains the correlation observed in the data (i.e. 0.43).

Second, the model generates the observed correlation between consumption and output in Mexico (0.76 vs. 0.78 in the data). Note also that, in both model and data, Mexican consumption is insigni...cantly correlated with US GDP. This indicates that US shocks do not contribute to the high volatility of Mexican consumption. This instead is the result of the response of Mexican consumption to domestic shocks.

A key driver of the volatility of consumption are the dynamics of the price of capital induced by domestic shocks. It is reassuring that the model matches closely the negative co-movement between Mexican output and the price of new capital (-0.45 vs. -0.54 in the data). Note also

> 32Note that the model also underpredicts the volatility of the extensive margin of trade, though given the distance between the measure in the model and in the data that should not be a surprise. Note also that, as discussed in section 4.2, the model generates a process for US consumption that is too volatile.

26
that the model generates an insigni...cant contemporaneous co-movement between the price of capital in Mexico and US GDP which is also consistent with the evidence (-0.13 in model vs. 0.13 in data). This is the case because, as we shall see below, US shocks a¤ect the price of new capital over the medium term but not so much contemporaneously.

Recall that the strong co-movement between US output and Mexican investment is the key driver of the large e¤ect that US shocks have on Mexican GDP. The model matches very closely the observed strong co-movement between Mexican investment and output in both the US (0.69 vs. 0.6 in the data) and Mexico (0.77 vs. 0.62 in the data).

Similarly, recall that the medium term productivity dynamics in Mexico result from the cyclicality of the ‡ow of intermediate goods that become exportable to Mexico (i.e. the extensive margin of trade). The model matches quite closely the co-movement between the growth in the number of varieties exported to Mexico (specially in durable manufacturing) and output in both the US (0.42 vs. 0.28 in the data) and in Mexico (0.42 vs. 0.42 in the data).

The model also broadly captures the cyclicality of the bilateral trade ‡ows which are also partly responsible for the co-movement between the US and Mexican GDPs. In particular the model captures the fact that Mexican imports from the US co-move more with Mexican GDP (0.82 vs. 0.93 in the data) than Mexican exports to the US (0.59 vs. 0.08 in the data). The model is also consistent with the strong co-movement of US GDP and both Mexican imports from the US (0.81 vs. 0.61 in the data) and exports to the US (0.56 vs. 0.68 in the data). Interestingly, .

Finally, the model captures the strong counter-cyclicality of Mexican trade balance. Specifically, the correlation between the Mexican trade balance as a share of GDP is -0.98 vs. -0.83 in the data. The model is also consistent with the higher (in absolute terms) correlation of the Mexican trade balance with Mexican GDP than with US GDP (-0.74 vs. 0.07 in the data).<sup>33</sup> It however generates FDI ‡ows that are too cyclical maybe because of the presence of a small but volatile component in actual FDI that does not respond to the US or Mexican business cycle.

# Inter-frequency co-movement

A ...nal fact presented in section 4.3 is the lead of US output over medium term ‡uctuations in Mexico. Table 3 explores the model’s ability to capture this fact. The ...rst row reports the empirical correlation between lagged HP-...ltered US output and the medium term component of Mexican output. The second row reports the average cross-correlation across 1000 simulations

> 33The higher counter-cyclicality of the Mexican trade balance with respect to US GDP in the model than in the data surely results from the lack of other international shocks.

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of the model. The model roughly captures the contemporaneous correlation between high frequency ‡uctuations in US output and medium term ‡uctuations in Mexican output (0.38 in the model vs. 0.28 in the data). More importantly, the model generates a hump-shaped cross-correlogram between these two variables as we observed in the data. However, in the data the peak correlation occurs after two years (0.53), while in the model it occurs on average after one (0.45).

A key prediction of our model is that the high frequency response of the extensive margin of trade to US shocks generates counter-cyclical ‡uctuations in the relative price of capital in Mexico over the medium term. The fourth row in Table 3 presents a quantitative evaluation of this prediction where we report the average correlation across our 1000 simulations between the medium term component of the Mexican relative price of capital and HP-...ltered US output at various lags. The correlation becomes more negative as we lag US GDP reaching a peak (in absolute terms) after two years (-0.42). This co-movement pattern matches quite closely the actual co-movement in the data reported in the third row of Table 3. There we can also see that the correlation between US GDP and the medium term component of the relative price of capital in Mexico gradually becomes more negative as we lag US GDP. The peak in reached at -0.5 with a 3-year lag of US GDP over the Mexican price of capital.

Mexican and US shocks have a di¤erent e¤ect on Mexican medium term ‡uctuations. Row 5 in Table 3 reports the actual correlation between HP-...ltered Mexican output at various lags and the medium term component of Mexican output. Though the contemporaneous correlation is positive it declines monotonically as we lag the series of HP-...ltered output.<sup>34</sup> Our model is consistent with this co-movement pattern since, unlike US shocks, Mexican shocks in our model do not induce a hump-shaped response of Mexican output (Figure 5). This is illustrated in row 6 of Table 3. The contemporaneous correlation between HP-...ltered and medium term Mexican GDP is 0.6 (vs. 0.45 in the data) and it becomes insigni...cant when lagging HP-...ltered GDP by two years (vs. one in the data).

Finally, in both, the model and the data (rows 7 and 8 in Table 3), we observe similar comovement pattern between HP-...ltered Mexican GDP and the medium term component of the Mexican price of capital. In both we observe that the counter-cyclicality of the medium term component of the price of capital in Mexico increases as we increased the lag reaching a peak of -0.34 after 2 years in the data vs. -0.52 after one year in the model.

> 34In table A4, we make a similar point by estimating VARs with HP-...ltered Mexican GDP and the medium term component of several Mexican variables (including GDP).

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## Implications for Aggregate Volatility

It is clear from Figure 1 that US shocks are a signi...cant source of volatility in Mexican GDP. But, what share of Mexican ‡uctuations is due to US shocks and what share is due to domestic shocks? Similarly, how much do Mexican shocks contribute to the volatility of US GDP?

Table 4 answers these questions by reporting the share of output volatility in each country attributable to each kind of shocks. The ...rst two columns focus on the volatility of HP...ltered output while the next two focus on the volatility of output over the medium term cycle. Consistent with Figure 5, Mexican shocks account for a small fraction of US ‡uctuations (3% at high frequency and 2% over the medium term cycle).

In contrast, US shocks represent a very signi...cant source of Mexican ‡uctuations. At the high frequency, 64% of Mexican GDP volatility is driven by US shocks, while over the medium term cycle, US shocks induce 66% of the volatility in Mexican GDP. This proves the importance of explicitly modelling the US economy to study the business and medium term cycles of the Mexican economy.

# 5 Conclusions

We have developed a two country asymmetric model to study the business cycle in developing countries. The model has two distinct elements for which we have plenty of micro evidence: the endogenous and slow di¤usion of technologies from the developed to the developing country and the presence of ‡ow adjustment costs to investment in the developing economy. When calibrated to the Mexican economy, our model generates three important features of Mexican business cycles.

First, US shocks have a larger e¤ect on Mexican than on US GDP. This result is driven by the larger amplitude of ‡uctuations in Mexican productivity and by the e¤ects that this has on investment. This ...nding has important implications for the sources of Mexican volatility. Despite the higher volatility of Mexican shocks, the di¤erential in GDP volatility between US and Mexico is due to the magnitude of the Mexican response to US shocks.

Second, the slow di¤usion of technologies to Mexico generates a hump-shaped response in Mexican output in response to US shocks. As a result, US shocks have more persistent e¤ects on Mexico than in the US. Further, this explains the observed lead of US GDP over the medium term component of Mexican output and the relative price of capital.

Third, consumption is no less volatile than output in Mexico. Our model accounts for this 29
stylized fact because a Mexican recession slows down the di¤usion of technologies to Mexico, generating a gradual increase in the price of installed capital. As a result, Mexican interest rates increase despite the lower marginal product of capital and consumption drops precipitously.

Of course to study how the extensive margin of trade and FDI respond to US shocks, it is necessary to model both the US and the Mexican economy. The complexity that entails developing a two country model of business cycles with endogenous technology is not trivial. However, by doing that we have not only been able to match the three stylized facts described above but have provided a quantitatively accurate account of high and medium term ‡uctuations in Mexico. A reasonable educated guess is that the mechanisms introduced in our model should provide an accurate account of business cycles in other developing countries.

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