Annex I. Shift-share Analysis of Investment Dynamics
This annex describes the methodology used for performing a shift-share analysis of the investment-to-output ratio dynamics.
Each sector can contribute to the investment-to-output ratio dynamics in two ways: by changes in investment within the sector (within-effect) and by changes in the share of the sector in aggregate output (between-effect, or structural shift). To decompose the contributions into within- and between- effects, we follow the shift-share methodology (see Busetti and others 2016 and EC 2017, among others).
The simplest way to illustrate the approach is to consider a one country, two-sector (i=[1, 2]), and two-period (t=[0, T]) model. Let Yi denote output in sector i, INVi denote investment, and superscripts 0 and T denote the beginning and the end of the period, respectively.
The aggregate investment-to-output ratio (I) at time T can be written as:
where Si denotes share of sector i output in total output. The difference in investment ratios at time 0 and T can be written as:
or alternatively as:
To make the decomposition invariant to a particular base, one could use period averages as weights by combining (1.2) and (1.3):
where bars indicate the arithmetic average over period [0, T].
In a multi-sector setting, expression (1.4) can be written as:
where N is the number of sectors. This breakdown could be used to gauge the magnitude of within-and between-effects.
Annex II. The Accelerator Model
Following IMF (2015) and EC (2017), we adopt the accelerator model to model investment. Investment in time t and country i (Iit) is a function of a desired stock of capital
The accelerator model postulates proportional relationship between changes in desired stock of capital and changes in output:
Plugging in (2.2) into (2.1), dividing both sides by Kit-1 and lagging the output by one year to alleviate the endogeneity issues yields the following baseline empirical specification:
where αi is the country-specific fixed effect and εit is the i.i.d. error.
Baseline regression (2.3) allows modeling the dynamics of investment based purely on output developments. The residual of this regressions would indicate whether the investment slowdown following the GFC can be largely explained by sluggish output developments. If that is not the case, then the baseline model can be augmented to include additional determinants of investment:
where P denotes additional factors driving investment, including those affected by policies. The significance of γs would help judging their importance in explaining the investment slowdown following the GFC.
The model is estimated using fixed effects panel estimator with standard errors corrected for autocorrelation, heteroskedasticity, and intra-group correlation. In some specifications, the regressions are run for a panel of sectors within countries (sector-specific fixed effects regressions) or for individual countries/sectors (time series regressions).
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Prepared by Tigran Poghosyan. In addition to the IMF’s Denmark team, I would like to thank Aqib Aslam, Romain Duval, Davide Furceri, Rasmus Mose Jensen, and seminar participants at the IMF’s European Department and Danmarks Nationalbank for helpful comments and suggestions.
From the capital dynamics equation: Kt = It + 6*Kt-i, where / denotes investment and 6 denotes the depreciation rate. Hence, a slowdown in / would directly translate into lower K.
Using output-to-hours worked ratio shows a smaller deceleration in labor productivity growth: from 1.1 percent in 2010 to 0.4 percent in 2016.
A similar picture emerges when doing a shift-share analysis for the 2008–16 period.
Other models include the Tobin’s Q, the neoclassical model, and various formulations of the Euler’s equation (see Oliner and others 1995 for a survey).
The uncertainty is most likely related to international developments rather than domestic factors.
Selected Issues Chapter “Danish Households, Asset Prices, and Interest Rate Shocks.”
Following the classification in the latest EIB report (EIB 2017), we compare Denmark with the following EU peers: Austria, Belgium, Finland, France, Germany, Luxembourg, the Netherlands, Sweden, and the United Kingdom.
The sectors are: (1) agriculture, forestry, and fishing, (2) mining and quarrying, (3) manufacturing, (4) electricity, gas, and water supply, (5) construction, (6) wholesale and retail trade, repair of motor vehicles and motorcycles, (7) transportation and storage, (8) accommodation and food service activities, (9) information and communication, (10) financial and insurance activities, (11) real estate activities, (12) professional, scientific, technical, administrative and support service activities, and (13) community social and personal services (see EUKLEMS for further information).
The categories are: (1) computing equipment, (2) communications equipment, (3) computer software and databases, (4) transport equipment, (5) other machinery and equipment, (6) total non-residential investment, (7) residential structures, (8) cultivated assets, (9) research and development, and (10) other intellectual property products (IPP) (see EUKLEMS for further information).
The author would like to thank Philippe Wingender for sharing his codes.
Ideally, we would have preferred to use different components of investment and leverage (corporate sector, households, etc.). However, such a breakdown is not available in the macro financial history database.
The database is available at: http://www.macrohistory.net/. 17 countries included in the sample are: Australia, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States.
Following Gaspar and others (2016), we exclude outliers of leverage (below 5th and above 95th percentiles).
A similar exercise for labor market reforms and employment was performed by Duval and others (2017).
See Selected Issues Chapter “Capital Income Tax Reform Options in Denmark” for details of tax policy measures.