What drives aggregate fluctuations? Given recent unpredictable events such as the COVID-19 pandemic and the Ukraine-Russia war, it is obvious that exogenous aggregate shocks drive substantial aggregate fluctuations. However, recent macroeconomic studies (e.g. Acemoglu et al. 2012) argued that microeconomic shocks at the firm level are also another important source of aggregate fluctuations. That is, unlike the classical diversification argument (e.g. Lucas 1977) that microeconomic shocks are averaged out at the aggregate level, the recent literature focuses on the propagation of microeconomic shocks through input-output linkages. It shows the possibility that microeconomic shocks could drive substantial aggregate fluctuations. This idea, called the micro-origin of aggregate fluctuations, has been widely accepted and created a new field of macroeconomics.

A number of theoretical papers analyse how aggregate fluctuations, especially the distribution properties of the GDP growth rate, are related to microeconomic shocks. Acemoglu et al. (2012) show that the variance of the GDP growth rate due to microeconomic shocks remains substantial when the structure of an input-output network is highly heterogeneous across firms. That is, when firms have many transactional relationships with other firms and lie at the heart of the network, microeconomic shocks to these hub firms cannot be cancelled out and are not negligible at the aggregate level. In addition, while Acemoglu et al. (2012) consider the variance (i.e. the second moment of the GDP growth rate), Acemoglu et al. (2017) study the tail probability driven by microeconomic shocks (i.e. the probability of the large deviation of the GDP growth rate) and argue that because of the heterogeneity of the network structure, microeconomic shocks contribute to the tail probability of the GDP growth rate. Furthermore, there are empirical studies that support the relevance of microeconomic shocks on aggregate fluctuations. For example, Miranda-Pinto (2021) uses OECD data at the sector level and shows that the change in input-output networks is the key to the decrease in the variance of the GDP growth rate over time. Magerman et al. (2016) analyse a firm-level input-output network based on Belgian tax data and quantify the variance of the GDP growth rate driven by microeconomic shocks.

Although the relevance of microeconomic shocks has been shared among economists, there are several remaining problems to be mentioned. In most of the theoretical studies, asymptotic results (e.g. the decay rate of the aggregate variance as the number of firms goes to infinity) have been discussed and used to argue the relevance of the micro-origin of aggregate fluctuations. For example, in Acemoglu et al. (2012), the main argument focuses on how rapidly the variance of the GDP growth decays as an input-output network becomes larger. However, the asymptotic results do not necessarily imply their corresponding non-asymptotic results (i.e. results with the input-output network fixed); that is, the asymptotic results do not tell us about the size of the micro-originated aggregate fluctuations given an empirical input-output network. In other words, there is a possibility that the size of the micro-originated aggregate fluctuations given an empirical network could turn out to be negligible despite the asymptotic results. Furthermore, to the best of our knowledge, there is no empirical work that studies a firm-level input-output network in terms of the "tail probability" of the GDP growth rate. In most of the empirical studies in the literature, the variance is used as the measure of the size of aggregate fluctuations, but, as Acemoglu et al. (2017) emphasise, the behaviour of the tail probability could be different from that of the variance. Therefore, we do not have a comprehensive picture of the micro-originated aggregate fluctuations with an empirical input-output network.

In Arata and Miyakawa (2021), we aim to fill this gap using Japanese firm-level data provided by Tokyo Shoko Research (TSR). This dataset contains firm-level information, such as sales and employees, and identifies the suppliers and customers of firms, from which we construct an input-output network covering more than 300,000 firms in Japan. Consistent with the previous studies, the input-output network in Japan is well connected, and the local network structure is highly heterogeneous across firms (see Figure 1). Based on this input-output network and structural models proposed in the literature (Acemoglu et al. 2012, and Baqaee and Farhi 2020), we calculate the impact of a microeconomic shock on aggregate output for each firm. Then, we complement the literature by focusing not only on the variance but mainly on the tail probability and distribution shape. Using the methods developed in Arata (2021), we quantify the size of the micro-originated aggregate fluctuations non-asymptotically based on the empirical input-output network.

**Figure 1** Input-output network in Japan in 2018

*Notes*: We include only firms with sales of more than 100 billion yen and input-output linkages among them. The size of each circle is proportional to the size of the firm it represents.

Our findings are as follows: Considering i.i.d. productivity shocks as microeconomic shocks, we find that the variance driven by microeconomic shocks is substantial despite the fact that the input-output network (and the number of firms) is large. This is due to the heterogeneity of the impact of microeconomic shocks across firms; that is, there are firms that have disproportionate impacts on the economy, and therefore, microeconomic shocks to these firms (especially large firms) do not die out even at the aggregate level. Because of this heterogeneity, the central limit theorem (CLT) does not hold, and the distribution of aggregate output does not converge to a Gaussian. We also find that this high heterogeneity comes mainly from the heterogeneity of the input-output network. Consistent with the recent literature, an input-output network is the origin of aggregate fluctuations.

However, in contrast to the variance, we find that microeconomic shocks contribute almost nothing to the tail probability of the GDP growth rate. Specifically, the tail probability driven by microeconomic shocks is negligible compared to its empirical counterparts (see Figure 2). Furthermore, we approximate the distribution of the GDP growth rate induced by microeconomic shocks (using Edgeworth expansion) and find that the approximated distribution is very close to a Gaussian. Note that this result does not contradict the finding that the CLT does not hold. This result means that given the empirical input-output network in Japan, the averaging effect still works even when the CLT does not hold, and microeconomic shocks cancel each other out to some extent. Therefore, the resulting distribution of aggregate output turns out to be close to a Gaussian.

**Figure 2** The approximation for the normalised aggregate output generated by microeconomic shocks

*Note*: The histogram of the empirical GDP growth rate is plotted for comparison.

These two results suggest that microeconomic shocks only cause small fluctuations of the GDP growth rate around its mean but do not explain its large deviation. In other words, given the empirical input-output network in Japan, the observed heterogeneity across firms is too low to explain the observed extremes of the GDP growth rate. In light of these non-asymptotic results, the role of microeconomic shocks in explaining aggregate fluctuations seems to be overestimated in the literature.

*Editor’s note: The main research on which this column is based (Arata and Miyakawa 2021) first appeared as a Discussion Paper of the Research Institute of Economy, Trade and Industry (RIETI) of Japan.*

## References

Acemoglu, D, V M Carvalho, A E Ozdaglar and A Tahbaz-Salehi (2012), “The Network Origins of Aggregate Fluctuations”, *Econometrica* 80(5):1977–2016.

Acemoglu, D, A Ozdaglar and A Tahbaz-Salehi (2017), “Microeconomic Origins of Macroeconomic Tail Risks”, *American Economic Review *107(1):54–108.

Arata, Y (2020), “The Role of Granularity in the Variance and Tail Probability of Aggregate Output”, RIETI Discussion Paper 20-E-027.

Arata, Y and D Miyakawa (2021), “An Empirical Analysis for the Micro Origin of Aggregate Fluctuations”, RIETI Discussion Paper Series 21-E-066.

Baqaee, D R and E Farhi (2020), “Productivity and Misallocation in General Equilibrium”, *Quarterly Journal of Economics* 135(1):105–163.

Carvalho, V M (2010), “Aggregate Fluctuations and the Network Structure of Intersectoral Trade”, working Paper, Universitat Pompeu Fabra.

Lucas, R E (1977), “Understanding Business Cycles”, In Carnegie-Rochester conference series on public policy, North-Holland.

Magerman, G, K D Bruyne, E Dhyne and J V Hove (2016), “Heterogeneous Firms and the Micro Origins of Aggregate Fluctuations”, NBB Working Paper No 312.

Miranda-Pinto, J (2021), “Production network structure, service share, and aggregate volatility”, *Review of Economic Dynamics* 39:146–173.