Short- and long-run heterogeneous investment dynamics

Abstract

In this paper, we model the dynamics of business investment taking into account asset-specific characteristics potentially affecting the reactivity of aggregate and disaggregate capital accumulation over the business cycle. We estimate Information and Communication Technologies (ICTs) and traditional investment (non-ICT) determinants within a Vector Error Correction Model testing the assumptions of the flexible accelerator and neoclassical model as well as the role of financial constraints and uncertainty. We evaluate our model on Italian data over the period 1980–2012, and we check our results also with Spanish and UK data. Our findings support the assumption that capital is heterogeneous since short- and long-run determinants are significantly different across the assets. Traditional assets experience stock adjustment costs while ICT investment incurs flow adjustment cost. In the short run, liquidity is a key determinant of investment independently of the asset type. In the long run, uncertainty significantly affects ICT. Finally, the results of the counterfactual exercises support the idea that ICT is a key policy variable to foster economic growth.

Appendices

This section draws substantially from Bacchini et al. (2013).

Appendix 1: Data sources

1.1 Italian (national) sources

1.1.1 Investments and capital stocks

Data for aggregate $(j = { agg})$ and disaggregate ($j = { me, nres, ict})$ capital stock and investments for the Italian case are drawn from ISTAT National Accounts (NA) and refer to the Italian business sector (i.e. they exclude public investments) over the period 1980–2012.

Series are available at both current prices and in volumes (chained index). Non-residential capital stock (nres) is the difference between business capital stock (agg), machinery, and equipment (me) and ICT (ict).

From the NA source, we can compute the series of capital stock and investments in volume, respectively, $K_t^j$ and $I_t^j$, and the corresponding series of investment deflators $P_t^j$, obtained as ratios between investments at current prices and those in volumes.

1.1.2 Output and the output gap

Output series $(Y_{t})$ is measured by GDP in volumes.

The output gap $({ YG}_{t})$ series is from the Ameco database of the European Commission. For the period

1.1.3 User cost of capital

In the user cost’s formula (3), $P_t$ is the GDP deflator; $\pi _t^j$ is the rate of change in investment prices (measured by $\Delta \log P_t^j )$; the rate of investments’ subsidies $(c_t)$ is the ratio between government subsidies to investments and the value of business investments in the previous year; the corporate tax rate $(\tau _t)$ is obtained by the series of effective tax rates from the NA source. The cost of borrowing $R_t^j$ is given by the average of the rate of interest of long-term government bonds (BTP) and ISTAT estimates of the rate of interest implicitly used in collecting information to compute capital stocks; the arbitrary risk premium ($\psi ^{j})$ is set to zero. Finally, depreciation rates are obtained by reversing the formula of the perpetual inventory method, as $\delta _t^j ={\left( {I_t^j -\Delta K_t^j } \right) }/{K_{t-1}^j }$.

1.1.4 Financial constraints and uncertainty

The degree of financial constraints (liq) is from the ISTAT monthly business survey where it is asked to the firms: “how do you judge the current level of liquidity (quite good, normal, bad)?”

The index of economic policy uncertainty (unc) is from Baker et al. (2016) over a period starting since 1997 (downloadable from http://www.policyuncertainty.com). Before 1997, unavailable uncertainty data are backward estimated by using the pattern of the GARCH component of the AR(2) representation of the GDP growth rate (over the period in which they overlap, the normalized data of the genuine uncertainty measure and of the estimated GARCH component evolve in a quite similar way).

1.1.5 R&D real spending and stock

Nominal R&D is measured by the total intramural R&D expenditure of the Italian business enterprise sector (source: Eurostat’s Statistics on Research and Development). R&D in real terms $(I_t^{berd} )$ is obtained by deflating its values with the GDP deflator. In order to compute the R&D stock, we used the perpetual inventory method with constant depreciation rate (assumed, as customary, equal to about 0.4—see, e.g. Hall 2007, and Bontempi and Mairesse 2015). In steady state, the initial value of the capital stock is proxied by $K_o^{berd} =I_o^{berd} /0.4$; although we acknowledge the crudeness of this assumption, its effect vanishes over a long time span like the one we have available.

1.2 Italy, Spain, and the UK data sources

EU KLEMS data are available for non-ICT and ICT capital stocks and investments over the period 1970–2009. These sources were updated with the corresponding growth rates from Eurostat source.

The uncertainty indicator and the R&D spending for Spain and the UK come from the same sources and procedures described above for Italy. All other series come from AMECO databank. In particular, R&D (berd) is measured by $\log \frac{I_c^{berd} }{Y_c }$, where $\frac{I_c^{berd} }{Y_c }$ is the ratio of R&D spending on GDP; the user cost (uc) cannot be fully asset-specific as it was in Tables 2 and 3 for Italy, because we had to proxy the inflation component of uc with the aggregate investment deflator. In addition, and more relevantly for the issues inspected, unavailable survey-based credit conditions (liq) are proxied here by two macrovariables: the interest rate $(R_{c}$, to proxy for credit market shocks), and the aggregate rate of gross operating surplus on the value added for the non-financial companies $({ gos}_{c}$, to proxy for the amount of internal funds).

Appendix 2: The investment capital stock system

The specification of the complete system for investments and capital stock is listed below. In the OLS estimate equations, the standard errors are reported in curly braces below each estimate. The use of OLS estimator is allowed by the weak exogeneity property emerged from the results in Sect. 4.2. Labels in capital letters denote variables in levels, while their logs are in small letters. Variables’ definitions and data sources are reported in “Appendix 1”.

1.1 Non-residential buildings (nres)

$$\begin{aligned}&\displaystyle \hbox {UC}_t^{nres} \equiv \left( {R_t^{nres} +\delta _t^{nres} -\Delta p^{nres}} \right) \left( {\frac{1-c_t }{1-\tau _t }} \right) \frac{P_t^{nres} }{P_t} \end{aligned}$$

(10)

$$\begin{aligned}&\displaystyle \Delta k_t^{nres} =\underbrace{0.068}_{0.031}+\underbrace{0.003}_{0.001}\times \Delta liq_t +\underbrace{0.107}_{0.029}\times \Delta y_{t-1} +\underbrace{1.045}_{0.136}\times \Delta k_{t-1}^{nres} -\underbrace{0.347}_{0.121}\times \Delta k_{t-2}^{nres} \nonumber \\&\displaystyle \qquad \qquad \qquad \qquad -\underbrace{0.002}_{0.001}\times \Delta uc_{t-2}^{nres} \underbrace{-0.023}_{0.010}\times \left[ {k_{t-1}^{nres} -\left( {\underbrace{0.750}_{0.088}\times y_{t-1} -\underbrace{0.100}_{0.031}\times uc_{t-1}^{nres} } \right) } \right] +\hat{{\varepsilon }}_t^{nres} \nonumber \\\end{aligned}$$

(11)

$$\begin{aligned}&\displaystyle I_t^{nres} \equiv \Delta K_t^{nres} +\delta K_{t-1}^{nres} \end{aligned}$$

(12)

1.2 Machinery, plants, and equipments (me)

$$\begin{aligned}&\displaystyle \hbox {UC}_t^{me} \equiv \left( {R_t^{me} +\delta _t^{me} -\Delta p^{me}} \right) \left( {\frac{1-c_t }{1-\tau _t }} \right) \frac{P_t^{me} }{P_t} \end{aligned}$$

(13)

$$\begin{aligned}&\displaystyle \Delta k_t^{me} =\underbrace{-0.597}_{0.160}+\underbrace{0.015}_{0.002}\times \Delta liq_t -\underbrace{0.013}_{0.006}\times \Delta unc_t +\underbrace{0.482}_{0.060}\times \Delta y_{t-1} +\underbrace{0.518}_{0.061}\times \Delta k_{t-2}^{me} \nonumber \\&\displaystyle \qquad \qquad \qquad \,\,-\underbrace{0.006}_{0.002}\times \Delta uc_{t-1}^{me} \underbrace{-0.087}_{0.023}\times \left[ {k_{t-1}^{me} -\left( {\underbrace{1.402}_{0.055}\times y_{t-1} -\underbrace{0.266}_{0.022}\times uc_{t-1}^{me} } \right) } \right] +\hat{{\varepsilon }}_t^{me}\nonumber \\ \end{aligned}$$

(14)

$$\begin{aligned}&\displaystyle I_t^{me} \equiv \Delta K_t^{me} +\delta K_{t-1}^{me} \end{aligned}$$

(15)

1.3 Information and communication technology goods (ict)

$$\begin{aligned}&\displaystyle \Delta i_t^{ict} =\underbrace{0.098}_{0.014}+\underbrace{0.113}_{0.026}\times \Delta liq_t +\underbrace{0.055}_{0.026}\times \Delta liq_{t-1} +\underbrace{0.044}_{0.026}\times \Delta liq_{t-2} -\underbrace{0.931}_{0.489}\times \Delta R_{t-1}\nonumber \\&\displaystyle \qquad \qquad \qquad +\underbrace{-0.115}_{0.032}\times \left[ {i_{t-1}^{ict} -\left( {y_{t-1} -\underbrace{1.127}_{0.166}\times unc_{t-1} +\underbrace{0.632}_{0.297}\times \log \left( {\frac{I_{t-1}^{berd} }{Y_{t-1} }} \right) +\underbrace{0.305}_{0.145}\times liq_{t-1} } \right) } \right] +\hat{{\varepsilon }}_t^{ict} \nonumber \\\end{aligned}$$

(16)

$$\begin{aligned}&\displaystyle K_t^{ict} \equiv I_t^{ict} +(1-\delta _t^{ict} )K_{t-1}^{ict} \end{aligned}$$

(17)

1.4 Aggregation through summation of the three business components (sum)

$$\begin{aligned}&\displaystyle K_t^{sum} \equiv K_t^{nres} +K_t^{me} +K_t^{ict} \end{aligned}$$

(18)

$$\begin{aligned}&\displaystyle I_t^{sum} \equiv \frac{I_t^{nres} \times P_{t-1}^{nres} +I_t^{me} \times P_{t-1}^{me} +I_t^{ict} \times P_{t-1}^{ict} }{P_{t-1}^{sum} } \end{aligned}$$

(19)

1.5 Aggregate modelling of business investments (agg)

$$\begin{aligned}&\displaystyle \hbox {UC}_t^{agg} \equiv \left( {R_t^{agg} +\delta _t^{agg} -\Delta p^{agg}} \right) \left( {\frac{1-c_t }{1-\tau _t }} \right) \frac{P_t^{agg} }{P_t } \end{aligned}$$

(20)

$$\begin{aligned}&\displaystyle \Delta k_t^{agg} =\underbrace{-0.081}_{0.021}+\underbrace{0.248}_{0.017}\times \Delta y_t +\underbrace{0.712}_{0.037}\times \Delta k_{t-1}^{agg} -\underbrace{0.009}_{0.002}\times \Delta uc_t^{agg} \nonumber \\&\displaystyle \qquad \qquad \qquad \underbrace{-0.038}_{0.010}\times \left[ {k_{t-1}^{agg} -\left( {\underbrace{1.141}_{0.058}\times y_{t-1} -\underbrace{0.170}_{0.044}\times uc_{t-1}^{agg} } \right) } \right] +\hat{{\varepsilon }}_t \end{aligned}$$

(21)

$$\begin{aligned}&\displaystyle I_t^{agg} \equiv \Delta K_t^{agg} +\delta K_{t-1}^{agg} \end{aligned}$$

(22)

Fig. 5

MeMo.It building blocks

Appendix 3: MeMo.It—ISTAT macroeconometric model

This section draws substantially from Bacchini et al. (2013).

MeMo-It belongs to a suite of economic forecasting models developed by Istat, where it plays a fundamental role in the modelling framework ensuring the overall consistency in the system. The model is composed by 53 stochastic equations and 78 identities, and represents a New Keynesian economic system including households, firms, public administration, and a foreign sector. It is an annual model that uses two sets of external (exogenous) information over the forecasting period. The first set refers to the main variables that characterize the development of the international scenario, such as trade growth, exchange rates, ECB interest rates, and the oil price. The second set instead includes annual estimates of key GDP components obtained from short-term models based on monthly and quarterly data available at the time of forecast. The main characteristic of MeMo-It is that it is strongly grounded in empirical information (data-based model) in order to assess the data admissibility of the theoretical assumptions and does not assume explicit microfoundations of weak form. Further, it has been thought as a simple and easy tool to be introduced to the users, and it is timely updated with the most recent release of National Accounts. This allows to deliver updated forecasts always coherent with the last vintage of NA figures.

MeMo-It is substantially based on the New Keynesian approach where the supply side of the economy plays a central role. Accordingly, the underlying key assumption is that in the short run, the economic activity is mainly driven by the demand side, while in the long run the economic system converges to potential output given by the supply side. Prices react to the output gap and, in this way, they accounts for the disequilibrium of supply and demand.

The dotted arrows in the lower portion of Fig. 5 represent the interactions arising from such disequilibrium (between the supply and demand rectangles) with the output gap (in the oval circle) which, in turn, affects the prices rectangle. In turn, price changes feedback into demand variables rectangle and into wages in the labour sector rectangle. Real wages and employment affect income distribution and households consumption (in the demand rectangle). Consumption and incomes in the demand rectangle are the tax bases which, combined with (exogenous) rates, define different forms of taxation in the government rectangle. Direct taxation and public transfers generate income redistribution that affects the demand, while indirect tax and social security contributions influence prices and labour cost. Finally, investments and output in the demand rectangle interact with the supply side through the accumulation of capital stock (lower arrow), and employment in the labour market rectangle (upper arrow).