RDP 2013-08: International Business Cycles with Complete Markets 1. Introduction

Business cycle predictions of two-country models are inconsistent with the data along several dimensions. Kehoe and Perri (2002) describe the ‘international co-movement puzzle’ (Baxter 1995) and the ‘quantity anomaly’ (Backus et al 1992, 1995) as the ‘… two major discrepancies between standard international business cycle models with complete markets and the data’ (p 907). The essence of the puzzles lies in the models' tendency to predict (i) negative cross-country correlations of investment and employment (the ‘international co-movement puzzle’); and (ii) international consumption correlations in excess of output correlations (the ‘quantity anomaly’). The opposite of both are observed in the data.

The literature has addressed these puzzles either by restricting the set of assets available in international financial markets (Baxter and Crucini 1995; Kollmann 1996; Kehoe and Perri 2002), by introducing new disturbances such as preference shocks, policy shocks and so on (Stockman and Tesar 1995; Ravn 1997; Wen 2007; Johri and Lahiri 2008), or both (Benigno and Thoenissen 2008). Our approach is different. We deviate from the assumption of time separable Cobb-Douglas preferences. This means that decisions today affect the choices available in the future. Our main result shows that a model with complete markets driven by productivity shocks alone can resolve the ‘international co-movement puzzle’.[1] In addition, our model outperforms standard models in accounting for the ‘quantity anomaly’.

We consider a one-good model with complete markets, costly capital adjustment and time non-separable preferences that allows arbitrarily small wealth effects on labour supply. Our model matches the data by predicting (i) positive cross-country correlations of investment and hours worked; and (ii) realistic cross-country correlations of consumption. It reduces the gap between international correlations of output and consumption, but fails to match the empirical regularity that the correlations of output are higher than those of consumption. In fact, the empirical performance of our model is remarkably similar to Kehoe and Perri's (2002) model with endogenously incomplete markets. Unlike models with restricted international markets, ours shows little sensitivity to the parameterisation of the forcing process.

Our model has three distinct features. First, it incorporates the preference structure introduced by Greenwood, Hercowitz and Huffman (1988) (henceforth GHH). Second, the model features internal habit formation in consumption. Third, like most international business cycle models, ours incorporates capital adjustment costs.

Introducing the GHH preference structure has two effects. First, in the absence of a wealth effect on labour supply, foreign individuals no longer reduce their hours in response to a positive productivity shock at home. To paraphrase Baxter and Crucini (1995, p 841), inhabitants in the less-productive country no longer ‘take a paid vacation’. Since innovations to productivity are contemporaneously correlated across countries, suppressing the wealth effect induces positive employment co-movement. Second, GHH preferences drive a wedge between the consumption behaviour at home and abroad. The response of output in the home country is greater than under standard preferences, leading to a stronger consumption response to productivity shocks. Foreign consumption responds less aggressively, resulting in a more realistic cross-country consumption correlation.

Internal habit formation introduces non-separability of preferences over time. Moreover, under GHH preferences, internal habit formation partially re-introduces the wealth effect on labour supply and intertemporal substitution in leisure. This addresses the concern that GHH preferences remove a potentially important mechanism (Greenwood et al 1988). The magnitude of both effects depends on the intensity of habit formation.[2]

Deviation from time separability of preferences alters the consumption dynamics. Habit-forming individuals internalise the negative effect their current consumption has on their future felicity. They aim to smooth not only consumption but also changes in consumption. To see how this transmission mechanism contributes to investment co-movement, consider the aftermath of a positive productivity shock at home. Domestic output jumps whereas consumption's response is hump-shaped: it increases gradually before falling. Consumers need time to adjust their habits, hence they save most of the extra output. This saving can be channelled into either investment or net exports. Since rapid changes in the capital stock are costly, only a fraction of the extra saving ends up being invested at home. Domestic absorption (output less net exports) rises gradually, while domestic output peaks on impact. Net exports increase, making additional resources available abroad. Although the wealth effect compels foreign agents to increase their consumption, habit formation dictates that they do so gradually. As long as the opportunity cost of not investing in the most productive location falls short of the capital adjustment cost at home, investment abroad also rises.

Our model relies on capital adjustment costs as in Hayashi (1982) to deal with excessive volatility of investment in response to productivity shocks. However, in our model sluggish capital adjustment has one more role to play. Capital adjustment costs interact with habit-formation preferences to deliver a hump-shaped response of domestic absorption to productivity disturbances. This feature is responsible for the positive international co-movement of investment.

In our model, the positive co-movement of hours reinforces the mechanism driving the positive cross-correlation of investment. As foreign hours do not fall following an increase in home productivity, there is a much larger response of global output. This creates savings that translate into foreign as well as home investment, augmenting the investment co-movement.

Our work is related to Devereux, Gregory and Smith (1992) who first introduced the GHH preference structure in a two-country business cycle model. Their model predicts a realistic international consumption correlation provided that productivity shocks are uncorrelated. More recently, Raffo (2008) demonstrated that an international real business cycle (RBC) model with GHH preferences and tradable intermediate inputs can be reconciled with the observed countercyclicality of net exports. However, the model fails to account for the ‘international co-movement puzzle’. Engel and Wang (2011) augment GHH preferences with consumption as a composite of durables and non-durables. Their two-country, two-sector model accounts for the observed procyclicality and volatility of imports and exports. Dmitriev and Krznar (2012) emphasise the role of time non-separable preferences in the international transmission of productivity shocks. Their model succeeds in matching the cross-country investment correlation at the cost of predicting almost perfectly negatively correlated hours worked. Both habit formation and GHH preferences have been used with relative success in small open economy models (Correia, Neves and Rebelo 1995; Mendoza 1991; Letendre 2004).

The rest of the paper is organised as follows. The next section describes the model economy. Section 3 discusses the parameterisation of the model. Section 4 presents our quantitative results and discusses how each feature of the model is essential for reproducing observed features of the data. Section 4.5 provides an overview of the sensitivity analysis. Section 5 offers some concluding remarks.


The importance of this result is emphasised by Baxter (1995, pp 1859–1860) who claims that ‘… a major challenge to the theory is to develop a model which can explain international comovement in labor input and investment’. In line with the above, Canova and Ubide (1998, p 558) argue that ‘… the magnitude and the sign of the cross-country investment correlations constitute an important regularity previously under-emphasized by the literature … For the largest 9 OECD countries the size of pairwise investment correlation ranges between [−0.01, 0.77] with the median value around 0.45. A successful model of the international business cycle must therefore be able to reproduce this important feature of the data …’. [1]

There seems to be little consensus in the empirical literature regarding the strength of the wealth effect on labour supply. On the one hand, Kimball and Shapiro (2008) report empirical evidence that the wealth effect is large, and is balanced by a similarly large substitution effect. On the other hand, Schmitt-Grohé and Uribe (2008) estimate the parameters of the utility function introduced by Jaimovich and Rebelo (2009) and find that the wealth effect is close to zero. [2]