1 Introduction

There is a large body of literature, which looks at the drivers of aggregate investment. The empirical models used in existing studies rely on the accelerator model or the standard neoclassical models of investment, and in some rare cases, on Tobin’s Q. Nevertheless, only a few studies analyse the relationship between product and labour market policies on the one hand and investment on the other. A large majority of the papers looking into the relationship between product market regulation and investment use sectoral and firm-level data. We only know of one paper (Kerdrain et al. 2010) that investigates the extent to which investment is associated with labour market regulations.

This paper seeks to contribute to the literature on the link between product and labour market policies and aggregate investment for 32 OECD countries over 1985 to 2013. We analyse the effects of product and labour market policies on investment. We also go beyond the usual linear relationship. First, we study whether policies amplify or attenuate each other’s effect on investment. We also test whether the relationship between policies and investment is non-linear in nature and whether the strength and direction of the relationship differs at different levels of regulation, and whether policy impacts are different when policies are being tightened or deregulated.

Our estimation results uncover a robust negative relationship between product and labour market policies and investment. Anticompetitive product market policies and more regulated labour markets tend to be associated with less investment. However, greater financial development, through an easier access to external finance, attenuates negative policy impacts. The estimation results provide evidence for non-linear policy effects and that the negative relationship between structural policies and investment is more pronounced if policies are being tightened rather than relaxed. We also show that product and labour market policies amplify each other’s negative effect on investment and that the quality of institutions matter for the impact of regulations.

The remainder of this paper is organised as follows. Section 2 summarises possible ways of modelling investment. Section 3 provides a literature overview on the relationship between structural policies and investment. Section 4 deals with econometric and data issues and discusses modelling choices. Section 5 reports the estimation results. Finally, section 6 provides concluding remarks.

2 Modelling Investment

2.1 The Accelerator Model

An accelerator model is a simple and commonly used way to model business investment.Footnote 1 It assumes that investment (I t ) can be split into net investment (I N) and replacement investment (I R). Replacement investment in period t equals the depreciation of the capital stock in t-1:

$$ {I}^R=\delta {K}_{t-1} $$
(1)

where δ is the depreciation rate. Net investment is assumed to equal to changes in the desired capital stock:

$$ {I}^N={\sum}_{i=0}^n{\beta}_i\Delta {K}_{t-i}^{\ast } $$
(2)

In turn, the desired stock of capital (K ∗) is considered to be a linear function of output (Y). Hence, real investment can be written as current and past real GDP growth and lagged capital stock:2

$$ {I}_t={\sum}_{i=0}^n{\beta}_i\Delta {Y}_{t-i}+\delta {K}_{t-1} $$
(3)

Equation (3) is usually estimated in constant domestic prices (Oliner et al. 1995; Lee and Rabanal 2010; Barkbu et al. 2015). It can be easily transformed into a net investment equation: \( {I}_t-\delta {K}_{t-1}={\sum}_{i=0}^n{\beta}_i\Delta {Y}_{t-i} \).

2.2 The User Cost of Capital

Obviously, investment can depend on more than just output growth and lagged capital stock. According to the neoclassical model, the desired stock of capital is not only a positive function of output but it also depends negatively on the user cost of capital (UCC) (Chirinko 1993; Oliner et al. 1995):

$$ {I}_t={\sum}_{i=0}^n{\beta}_i\Delta \left({Y}_{t-i}{UCC}_{t-i}^{-\sigma}\right)+\delta {K}_{t-1} $$
(4)

where σ is a constant elasticity of substitution between capital and labour in the production function (Chirinko 1993). Tevlin and Whelan (2003) argue that the capital stock is a non-stationary variable and propose a stationarised variant of eq. (4) in growth rates:

$$ \frac{I_t}{K_{t-1}}=\propto +{\sum}_{i=0}^n{\beta}_i\Delta {y}_{t-i}+{\sum}_{i=0}^n{\gamma}_i\Delta {ucc}_{t-i} $$
(5)

Fundamentally, there exists a long-run relationship linking the desired stock of capital to the level of output and the user cost of capital, which can be written as follows:

$$ {K}_t^{\ast }=\alpha {Y}_t\bullet {UCC}_t^{-\sigma } $$
(6)

Log-linearisation and the error correction representation give the following equation:3

$$ \Delta {k}_t=\gamma {k}_{t-1}+\beta {y}_{t-1}+\delta u{cc}_{t-1}+\theta \Delta {y}_t+\pi \Delta u{cc}_t $$
(7)

2.3 Tobin’s Q and Euler Equations

Alternative models of business investment are Tobin’s Q model and Euler equations. Tobin’s Q links investment to the ratio of market value of corporate assets to the replacement cost these assets. Euler equations are based on a dynamic optimisation problem of a representative firm wanting to maximise its present value and describe investment to its past linear and quadratic form (Bond and Meghir 1994).

2.4 Investment and Structural Policies

Investment and capital deepening can depend on country characteristics including the ease with which funding is available to business. The business environment is also an important factor. If the direct and indirect costs of starting a business are low, the number of business start-ups will increase (World Bank 2014). This in turn can translate into more investment. Similarly, pro-competitive product market regulation is likely to push firms to invest more to stay ahead of competitors or allow the entry of new competitors willing to invest. Less relaxed labour market regulations allow for a less costly reallocation of capital and labour within and across firms and could, by lowering adjustment costs, encourage investment.

To account for the impact of structural policies on the long-run level of investment, eq. (6) could be augmented by product and labour market regulations, as in eq. (8):

$$ K=f\left(Y,{UCC}^{-\sigma }, PMR, LMR\right) $$
(8)

where PMR and LMR refer to product and labour market regulations. Pelgrin et al. (2002) use a similar line of reasoning to plug in financial development as a driver of long-term business investment into the neoclassical investment model.Footnote 2

3 Literature Overview of Aggregate Investment Models

3.1 The Comparative Performance of Benchmark Investment Models

The consensus view emerging from the empirical literature is that Euler equations have not been very successful in explaining aggregate investment and perform poorly in forecasting aggregate investment (Oliner et al. 1995). Another common finding is that the Q model often fails to explain investment at the macroeconomic level (Oliner et al. 1995; Philippon 2009). Philippon (2009) argues that using a Q ratio based on bond prices rather than equity prices helps improve the fit of aggregate investment equations. The difficulty with Tobin’s Q at the macro level is that it can be constructed using firm level data on listed companies. Those data may not be representative for countries with predominantly bank finance. Also, market valuation of the assets of non-financial corporation at the macroeconomic level is bound to be subject to measurement errors, partly arising from equity market bubbles. Nevertheless, recent empirical work by the IMF (Lee and Rabanal, 2010; Barkbu et al., 2015) relied on the Q model for aggregate investment.

The empirical results on the neoclassical model are not much less controversial. It is difficult to identify sizeable negative effects of the cost of capital on aggregate investment. Several reasons may explain this finding. First, aggregate business investment may be unresponsive to the cost of capital due to aggregation bias. Such a bias can arise if different components of aggregate investment, such as investment in producers’ durable equipment, ICT or commercial or industrial structures react differently to the cost of capital. Indeed, the elasticity to the cost of capital of investment in computers is considerably higher than that of aggregate investment (Tevlin and Whelan 2003). Second, the elasticity of investment to the cost of capital can be low because estimations are usually carried out for the dynamic relationship, that is for investment and changes in the cost of capital.

Yet looking at the long-term relationship between the stock of capital and the cost of capital in a cointegration framework may yield higher elasticities. In addition, OLS estimates often reported in the literature tend to underestimate the elasticity due to a small sample bias. Caballero (1994) shows that this bias is very large for the case of the US economy. Nevertheless, this result cannot be generalised for a more recent and longer period. Lee and Rabanal (2010) reports considerably lower elasticities than Caballero (1994). Third, results reported in Tevlin and Whelan (2003) suggest that the small effect of the cost of capital on investment is largely a result of the low interest rate elasticity. Separating the cost of capital into relative prices and the interest rate component shed light on a sizeable negative correlation between relative prices and investment. By contrast, the interest elasticity of investment is close to zero (Tevlin and Whelan 2003). Studies looking at different periods and a variety of countries confirm this finding (Banerjee et al. 2015; and Barkbu et al. 2015) or even find a positive correlation between interest rates and investment (Kothari et al. 2014). Explanations for the missing interest rate effects range from simultaneity bias to the fact that aggregate interest rate series do not reflect the interest component of investment (Sharpe and Suarez 2014).

A systematic comparison of alternative models indicates that the accelerator model outperformed the other investment models until the early 1990s (Oliner et al. 1995). Nevertheless, the accelerator model had problems of capturing the investment boom in the mid- and late-1990s. The failure of the accelerator model arises from the substantial rise in investment in computer equipment, which, through composition effects, increased the average depreciation rate. Separating computer and non-computer investment helps regain confidence in the accelerator model (Tevlin and Whelan 2003).

Overall, most studies looking into the impact of structural policies on investment are not fully in line with the reference investment models. The dependent variable is investment as a share of GDP or as a share of the capital stock. The accelerator model and its augmented versions use the real capital stock as a dependent variable. The accelerator model includes real GDP as a regressor. This variable is often missing from the empirical estimations. In addition, the lagged dependent investment variable is also very frequently included in empirical models of investment. The accelerator model and its extensions would not contain this variable.

3.2 Investment and Structural Policies

3.2.1 Product Market Regulation

The literature looking into the structural drivers of aggregate investment is relatively thin. There is some empirical evidence that the degree of product market regulation correlates with investment outcomes. Nevertheless, this link is not very robust. A majority of papers analysing the connection between product market regulation and investment relies on sectoral data. Two of them (Alesina et al. 2005; Égert 2009) look only at the seven network sectors for which the OECD’s Energy Transport and Communications Regulation (ETCR) indicator is available: electricity and gas, post and telecommunications, road freight, air and rail transport. They find a strong negative correlation between barriers to entry and investment: higher barriers to entry are associated with lower investment in those sectors. Vartia (2008) covers all sectors of the economy and employ the OECD’s regulatory impact indicator. This indicator captures the extent to which any given sector is influenced by regulation in network industries through intermediate inputs. The results tend to show a negative relationship but they are not overly robust to alternative model specifications. Another string of papers uses firm-level data in network industries and report mixed results. Araújo (2011) is able to identify some weak negative relationship between barriers to entry and investment but Cambini and Rondi (2011) cannot pin down such a relationship between overall regulation and public ownership on the one hand and investment on the other.

Kerdrain et al. (2010), the only paper looking at country-level investment, report statistically significant coefficient estimates on the OECD’s ETCR indicator for a panel of OECD countries. By contrast, extending the sample to 117 countries and using components of the World Bank’s Doing Business indicator, they shed light on a negative and precisely estimated relationship between investment and the number of procedure to register a business and the cost of starting a business. The coefficient estimates on the overall Doing Business indicator are statistically not significant. The same applies to the indicator measuring the days required to start a business.

3.2.2 Labour Market Regulation

At the macroeconomic level and for several OECD countries, there is no evidence that labour market regulation has any impact of investment. Kerdrain et al. (2010), the only paper adding an indicator of labour market regulation to an investment equation finds statistically non-significant coefficient estimates for the overall Employment Protection Legislation (EPL) indicator as well as for its components on temporary and permanent contracts.

There is mixed evidence on the relation between capital stock and labour market regulation at the firm level.Footnote 3 Autor et al. (2007) document for US firms that higher firing costs (wrongful discharge exceptions) are linked to higher capital stock and capital-to-labour ratios. But they show that the effect becomes negative when state-specific trends are used. The paper also suggests that a rise in capital may be related to a correction of an earlier downturn and that the introduction of more stringent firing regulations followed a rise of the capital-to-labour ratio. Using a panel of European firms, Cingano et al. (2010) find that more stringent EPL reduces investment per worker and capital per worker. By contrast, focusing only on Italian firms, Cingano et al. (2015) show that the introduction of unjust-dismissal costs raises the capital-to-labour ratio in firms with less than 15 employees, compared to larger firms.

3.2.3 Financial Development

Past work has analysed the relation between financial development and investment. This strand tends to find that more developed capital markets and an easier access to bank credit, usually captured by the private credit to GDP ratio, tend to go hand in hand with a higher level of investment. Both Bassanini et al. (2001) and Pelgrin et al. (2002) report for a set of industrialised OECD countries a strong positive correlation between stock market capitalisation and private credit over GDP on the one hand, and private business investment on the other hand. For a more recent sample and aggregate investment rather than private business investment, Kerdrain et al. (2010) identify a positive correlation between financial liberalisation and investment but could not find a statistically significant positive correlation between stock markets (market capitalisation and turnover) and investment. Salotti and Trecroci (2012) also find it difficult to pin down a positive relation between private credit and investment. Identifying a strong positive correlation between financial development and investment is not an easy task for emerging and developing countries. For instance, Luca and Spatafora (2012) and Lim (2014) report weak evidence for such a link for panels including over 100 countries. Empirical evidence in Ghura and Goodwin (2010) is mixed for a group of 31 emerging and developing countries.

4 Modelling and Data Issues

4.1 Testable Equations

4.1.1 Linear Specifications

Our baseline equation includes the real stock of capital as the dependent variable. Real output, the user cost of capital and product market regulation are used as regressors:

$$ {K}_{j,t}=f\left({Y}_{j,t},{UCC}_{j,t},{PMR}_{j,t}\right) $$
(9)

Equation (9) implies that the capital stock depends on the level of real output, user cost and the level of product market regulation. The user cost of capital is decomposed into i.) long-term real interest rate, ii.) corporate taxes, and iii.) relative investment prices. The level of the stringency of product market regulation is captured by the OECD’s Energy Transport and Communications Regulation (ETCR) indicator. Tighter regulation can be expected to result in less investment and a lower capital stock in the long run.

Equation (9) is augmented by including labour market regulation (LMP):

$$ {K}_{j,t}=f\left({Y}_{j,t},{UCC}_{j,t},{PMR}_{j,t},{LMP}_{j,t}\right) $$
(10)

Labour market regulations are measured by four indicators drawn from OECD data sources: the tax wedge, the Employment Protection Legislation (EPL) indicator (for permanent contracts), the unemployment benefit replacement rate (UBRR) and spending on active labour market policies (ALMP). Higher values of the first three variables indicate more strict regulation. Higher labour market regulation is expected to be correlated with a lower capital stock. The rise in the last indicator, through facilitating labour reallocation, is thought to be positively correlated with the capital stock.

Finally, measures of financial development (FD) such as private credit to the economy and measures of stock market deepening (stock market capitalisation and turnover) are added to eq. (10):

$$ {K}_{j,t}=f\left.\left({Y}_{j,t},{UCC}_{j,t},{PMR}_{j,t},{LMP}_{j,t},{FD}_{j,t}\right)\right) $$
(11)

4.1.2 Non-linear Specifications

Smooth and Threshold non-linearities and Asymmetric Effects

Policies could have an increasingly or decreasingly negative impact on the capital stock (smooth non-linearity, eq. 12).

$$ {K}_{j,t}=f\left({Y}_{j,t},{UCC}_{j,t},{PMR}_{j,t},{LMR}_{j,t},{FD}_{j,t},{PMR}_{j.t}^2,{LMR}_{j,t}^2,{FD}_{j,t}^2\right) $$
(12)

Also, the impact of regulation could be different at high and low levels of regulation (threshold non-linearity). Eq. (13) shows this type of effect when the variable of interest has different coefficients below and above the tipping point of the threshold variable. If the threshold variable is the same variable, this is a classical ‘univariate’ non-linear effect. If the threshold variable is another policy variable, the results are comparable to interactions. For instance, the impact of labour market policies could depend on the level of restrictiveness of product market regulation. The threshold value is determined endogenously through a grid search: A grid search with steps of 1% of the distribution is carried out to find the value of the threshold variable that minimises the sum of squared residuals of the estimated two-regime model. The grid search starts at 15% of the distribution and stops at 85% to ensure that a sufficient number of observations falls into each regime. There is evidence for non-linearity if the null hypothesis of β 1 = β 2 can be rejected against the alternative hypothesis of β 1 ≠ β 2. First, the time-varying variables will be used as threshold variables. Second, the time-invariant variables and the country averages of the time-varying variables will also be used as threshold variables.

$$ {K}_{j,t}=\left\{\begin{array}{ccc}\hfill {\alpha}_1+{\alpha}_2{Y}_{j,t}+{\alpha}_3{UCC}_{j,t}+{\alpha}_4{LMR}_{j,t}+{\alpha}_5{FD}_{j,t}+,{\beta}_1{PMR}_{j,t}+{\varepsilon}_t\hfill & \hfill if\hfill & \hfill PMR<T\hfill \\ {}\hfill {\alpha}_1+{\alpha}_2{Y}_{j,t}+{\alpha}_3{UCC}_{j,t}+{\alpha}_4{LMR}_{j,t}+{\alpha}_5{FD}_{j,t}+,{\beta}_2{PMR}_{j,t}+{\varepsilon}_t\hfill & \hfill if\hfill & \hfill PMR\ge T\hfill \end{array}\right. $$
(13)

Finally, the impact of regulation could be different depending on the direction of the change in regulation, e.g. if regulation is being tightened or relaxed (asymmetric effect). Eq. (14) helps test these non-linear effects. Again, we can conclude in favour of an asymmetric effect if the null hypothesis of β 1 = β 2 can be rejected against the alternative hypothesis of β 1 ≠ β 2.

$$ {K}_{j,t}=\left\{\begin{array}{ccc}\hfill {\alpha}_1+{\alpha}_2{Y}_{j,t}+{\alpha}_3{UCC}_{j,t}+{\alpha}_4{LMR}_{j,t}+{\alpha}_5{FD}_{j,t}+,{\beta}_1{PMR}_{j,t}+{\varepsilon}_t\hfill & \hfill if\hfill & \hfill \varDelta PMR<0\hfill \\ {}\hfill {\alpha}_1+{\alpha}_2{Y}_{j,t}+{\alpha}_3{UCC}_{j,t}+{\alpha}_4{LMR}_{j,t}+{\alpha}_5{FD}_{j,t}+,{\beta}_2{PMR}_{j,t}+{\varepsilon}_t\hfill & \hfill if\hfill & \hfill \varDelta PMR\ge 0\hfill \end{array}\right. $$
(14)

Policy Interactions: The Long-Term Effect

The impact of one policy could depend on the level of another policy. Threshold regressions allow for two (or more) regimes. Using interactions in the regressions would allow a smoother dependence on the threshold variable. For instance, interacting the time-varying ETCR indicator with a measure of EPL, which is calculated as a country average over the sample period (and demeaned across countries) would tell us by how much the overall coefficient on ETCR would change if a country moves away from the cross-country average (eq. 15a).

This type of analysis can be extended to the time-invariant measures of product market regulations (PMR subcomponents), measures of the ease of doing business and indicators capturing the quality of institutions. Some policies such as institutions change slowly over time and can be observed at high intervals or we only have a couple of observations of them. These variables cannot be used as determinants of investment in regressions with country fixed effects (because country fixed effects capture these variables) but could be interacted with the time varying variables. In this case, the interaction term would tell whether the impact of a product or labour market policy would depend on the level of these institutions or other policies (eq. 15b).

$$ {K}_{j,t}=f\left({Y}_{j,t},{UCC}_{j,t},{PMR}_{j,t},{LMR}_{j,t},{FD}_{j,t},{PMR_{j,t}}^{\ast}\overline{LMR_j}\right) $$
(15a)
$$ {K}_{j,t}=f\left({Y}_{j,t},{UCC}_{j,t},{PMR_{j,t}}^{\ast}\overline{INSTITUTIONS_j}\right) $$
(15b)

Policy Interactions: The Impact on the Speed of Adjustment

Finally, cross-country variations in policies and institutions could also have an influence on the speed of adjustment in the error correction model. In such cases, the time which is required to reach the long-run equilibrium will depend on the level of policies across countries (the deviation from the cross-country mean). This relationship is estimated based on eq. (16) below where \( {\widehat{\varepsilon}}_{t-1} \) is the lagged deviation from equilibrium obtained from the first-stage long-term model of our estimation strategy (see section 4.4):

$$ \varDelta {K}_{j,t}=f\left({\widehat{\varepsilon}}_{t-1},{{\widehat{\varepsilon}}_{t-1}}^{\ast}\overline{INSTITUTIONS_j}\right) $$
(16)

4.2 Data Sources and Definitions

The capital stock series are drawn from OECD databases and relate to business capital stock (total minus housing). The component of the user costs of capital, that is the long-term real interest rate, relative investment prices and corporate taxes are calculated using data obtained from various OECD databases (see Tables 1 and 2).

Table 1 Empirical estimations including product and labour market regulation indicators
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Table 2 Variable definitions and sources
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The baseline models are estimated for a panel including 32 OECD countries and covering the period from 1985 to 2013. The corporate tax variables are not available for Mexico and Chile. This reduces our sample from the complete sample of 34 OECD countries to 32 (all other variables are available for all OECD countries). Our sample period is relatively short, encompassing just about 30 years, because the capital stock series obtained from OECD sources start in 1985. Otherwise, most other variables, except the stock market indicators, are available at least from the mid-1970.

More stringent regulation in various parts of the economy, including labour and product markets, can impede efficient allocation of capital and labour within and across firms and industries. This can impact negatively on investment. Product market regulation could be captured by the OECD’s Product Market Regulation (PMR) indicator or the World Bank’s Doing Business indicator. The drawback of the PMR indicator is that it is available every five years (1998, 2003, 2008 and 2013).Footnote 4 The Doing Business indicators are available at annual frequency. However, it only covers the period from 2002 to 2014.

The OECD’s energy, transport and communications regulation (ETCR) indicator, a subset of the OECD’s Product Market Regulation (PMR) indicator, covers a longer period as it starts in 1975 and ends in 2013.Footnote 5 It also has annual observations. For these two reasons, this paper uses the ETCR indicator, which measures the degree of product market regulation on a scale of 0 to 6. Low numbers indicate less regulation, higher numbers refer to more stringent regulation.

In addition to product market regulation, labour market regulation can also bear an impact on MFP through the direct effects of the allocation of labour resources and the indirect impact on capital reallocation. Therefore, we use four indicators capturing labour market regulation: i.) tax wedge, ii.) spending on active labour market policies (ALMP), iii.) the employment protection legislation (EPL) indicator (for permanent contracts), and iv.) the gross unemployment benefit replacement rate. These data series are borrowed from Gal and Theising (2015), which provide details on data sources and definitions.Footnote 6

In line with the literature, three measures of financial system development are used: private credit to GDP to measure the ease of access to bank credit, and two measures of stock market deepening: stock market capitalisation and stock market turnover as a share of GDP. The original private credit to GDP series obtained from the World Bank’s World Development Indicators (WDI) database contains very sharp changes for some countries. The stock market indicators are shorter than any other variables. To limit the loss of observations, they will not be used in a systematic fashion.

Four groups of time-invariant variables are interacted with the time-varying product and labour market regulation indicators.

  • The first group includes the country averages of the time varying policy variables (such as ETCR and EPL).

  • The second group relates to sub-groups of the OECD’s Product Market Indicators (PMR). The headline PMR indicator and its two-level disaggregated sub-indices (state control, barriers to entrepreneurship; and barriers to trade and investment)Footnote 7 are used. These series are available from 1998 to 2013 at five year intervals. For each country, the average of the available observations is employed.

  • The third group includes the ease of doing business (the time and cost of insolvency and starting a business). These data are obtained from the World Bank’s World Development Indicators database.

  • The fourth group includes variables capturing the quality of institutions (e.g. rule of law and the quality of the legal system). The rule of law variable comes from the World Bank’s World Development Indicators database. The quality of the legal system is drawn from the Fraser Institute’s Economic Freedom of the World database. For each country, the mean of the available observations is calculated and used in the estimations.

4.3 Descriptive Statistics and Preliminary Data Analysis

Table 3 provides some descriptive statistics of the capital stock series, the policy variables and the control variables.Footnote 8 A number of interesting features emerge. Looking at the various measures of standard deviation indicates that the capital stock, the real GDP series and to a lesser extent the EPL indicator vary a lot across countries with much less so over time (once country fixed effects are taken out of the series). At the same time, most of the policy variables exhibit a substantial average within-country (as opposed to cross-country) variation, even after controlling for common year fixed effects. Table 4 gives an overview of the cross-country features of the time-invariant variables.

Table 3 Descriptive statistics – time-varying variables
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Table 4 Descriptive statistics – time-invariant variables
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Figure 1 shows the ranking of countries for the PMR sub-indicators and selected institutional variables. Several observations deserve mention. First, the scope of state control is higher in all countries when compared to barriers to entry & entrepreneurship and barriers to trade and investment. Cross-country variation in this variable is also higher. State control is the lowest in Anglo-Saxon countries, Estonia and Japan. It is particularly high in Southern Europe, Israel and Poland. By contrast, barriers to trade and investment are relatively low for all countries, particularly for selected euro area countries, the UK and Denmark. While cross-country variations are also smaller, Canada, Turkey, Korea and Mexico have substantial restrictions. A clear pattern emerges for the variables capturing the quality of institutions. Nordic countries tend to have the best institutions. Southern and Eastern European countries have less robust institutions than advanced OECD economies. Turkey and Mexico have the weakest institutions.

Fig. 1
figure 1

Product market regulation and the quality of institutions in OECD countries sample average. Note: Higher figures indicate more stringent regulation for the PMR indicators. Higher numbers reflect a higher quality of institutions measured by the rule of law and the legal system variables

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The panel unit root tests are carried out to investigate the order of integration of the variables used in the empirical analysis. The Im-Pesaran-Shin test Im et al. (2003) (IPS) panel unit root test is applied to the series used in the regression analysis. The IPS test allows for heterogeneity across countries in the autoregressive coefficient and the lag length used for individual countries. It tests the null hypothesis of a unit root against the alternative of the absence of a unit root. A model with a trend and a constant and a model with only a constant are used.

The following patterns emerge from the IPS test for 32 OECD countries for the period of 1985 to 2013 (Tables 5 and 6). First, the tests show that the majority of the variables are integrated of order 1: they have a stochastic and/or a deterministic trend in levels. Second, a few variables are found to be stationary in levels. That the output gap has no unit root comes without surprise. The other stationary variable is the spending on ALMP. Second, the IPS test indicates the absence of a unit root for all first- and second-differenced variables.

Table 5 Correlations
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Table 6 Im-Pesaran-Shin (IPS) panel unit root tests 32 OECD countries (MEX, CHL excluded), 1985–2013
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4.4 Estimation Methods

Given the non-stationary nature of the data, cointegration techniques are needed to estimate the level relationships linking the capital stock with its long-term drivers. If the variables are not related through a cointegrating vector, the estimated level equations may be spurious.

The long-term coefficients are estimated on the basis of the Dynamic OLS (DOLS) estimator. Over the standard OLS estimator, it has the advantage that it corrects for the possible endogeneity of the regressors and autocorrelation in the residuals by incorporating leads and lags of the regressors in first differences (Stock and Watson 1993):

$$ {Y}_{j,t}={\beta}_0+\sum_{i=1}^n{\beta}_n{X}_{j,i,t}+\sum_{i=1}^n\sum_{l=-{k}_1}^{k_2}{\gamma}_{i,l}\varDelta {X}_{j,i,t-l}+{\varepsilon}_t $$
(17)

where Y t is the capital stock and \( \overline{X} \) is the vector of capital stock drivers. j stands for individual countries, i for the regressors, l for the leads and lags and k1 and k2 represent respectively the maximum leads and lags. Eq. (17) are estimated using country and time fixed effects.

Whether or not the variables of interest are cointegrated can be tested in two ways. First, the residuals obtained from the long-term relationship (ε t ) can be used to estimate the error correction model in the second stage. Weak evidence for the presence of cointegration is if the error correction term in this second stage is statistically significant and has a negative sign. This implies an error correction mechanism to be in place. A second and more formal test of cointegration is when the estimated residuals from the long-term relationship are tested for the presence of a unit root. The rejection of the null hypothesis of a unit root can be interpreted in favour of cointegration, in the spirit of the Engle and Granger residual-based cointegration approach. Here we use Kao’s residual-based panel cointegration tests (Kao 1999), which, along with eq. (1), allows for country-specific intercepts but imposes homogenous coefficients.

Our modelling framework relies on a two-stage error correction model. Modelling investment could also be based on a single-equation error correction model, along the lines of eq. (18):

$$ \Delta {K}_t=c+\gamma {K}_{t-1}+{\sum}_{i=1}^n{\beta}_i{X}_{i,t-1}+\mu \Delta {K}_{t-1}+{\sum}_{i=1}^n{\delta}_i\Delta {X}_{i,t}+{\sum}_{j=1}^m{\theta}_j{Z}_{j,t}+{\varepsilon}_t $$
(18)

where \( \gamma {k}_{t-1}+{\sum}_{i=1}^n{\beta}_i{x}_{i,t-1} \) gives the long-run relationship including the n long-term covariates, \( {\sum}_{i=1}^n{\delta}_i\Delta {x}_{i,t} \)are the dynamic terms of the long-run variables such as real output, UCC and ETCR. \( {\sum}_{j=1}^m{\theta}_j{z}_{j,t} \) is the additional set of m covariates entering the short-term dynamics.

Nevertheless, the two-stage approach provides more flexibility for our purpose compared to a single-equation error correction model. Importantly, the two-stage approach allows for putting country and year fixed effects in the long-run relationship and for including only country fixed effects in the short-term dynamics. In the single-equation approach, one can put either only country fixed effects or country & year fixed effects both in the long-run and short-run relationship. To illustrate the lack of flexibility of the single-step approach is when one wants to use a measure of common trend (capturing for instance global uncertainty in the short-run dynamics). It can be used only without year fixed effects, but this would mean that year fixed effects would not be included in the long-run relationship.

5 Estimation Results

The standard investment model works fine: only the real interest rate is found weakly related to the capital stock. We first estimate an investment model which links the level of capital stock to the level of output and the components of the user cost (long-term real interest rates, corporate taxes and relative investment prices). All regressions include the output gap to control for cyclical fluctuations in the dependent and independent variables. Output has a positive and almost unity correlation with the capital stock. Long-term real interest rates, the corporate taxes-to-GDP ratio and the relative investment price variable bear the expected negative sign.Footnote 9 However, the corporate tax variable and to some extend the real interest rate variable are not always statistically significant.. To be fully consistent with theory, we keep all three components of the user cost of capital in the specifications augmented by structural policy indicators.

5.1 Product Market Regulation

Product market regulation, measured by the OECD’s ETCR indicator, shows a fairly robust negative relationship with the capital stock series. We proceed step by step by augmenting the standard investment model by structural policy indicators. We first add the ETCR indicator. It has a strong negative correlation with the capital stock. Estimation results reported in Table 7 suggest that on average, a 1% decrease in the (log) ETCR indicator is associated with an increase of somewhere between 0.04% and 0.05% in the capital stock (columns 2 to 5). The relationship holds if the capital stock is regressed on the log-level rather than the level of the ETCR indicator (column 1). The results are also fairly robust if the sample is reduced to the pre-crisis period (1985 to 2006 from 1985 to 2013, columns 3 and 4) or if the country coverage is reduced (column 5). The regressions are also carried out using the capital stock-to-GDP ratio (the real output variable is dropped as a regressor). The results are robust when using ETCR in levels (columns 7 to 10) but the standard errors are very large for log-level ETCR indicator (column 6).

Table 7 Product market regulation, 1985–2013
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5.2 Labour and Product Market Regulations

The employment protection legislation (EPL) indicator has a strong and quantitatively important negative relationship to the capital stock (Table 8). This is an interesting result given the mixed evidence emerging from the firm-level studies mentioned earlier (Autor et al. 2007 and Cingano et al. 2010; Cingano et al. 2015). We carried out a number of robustness checks. First, we used both the level and log-level of EPL. Second, we reduced our country coverage. Third, we employed the capital stock-to-labour ratio used in the above mentioned studies as dependent variable. Finally, we also ran regressions including only EPL as explanatory variables (but keeping the country and year fixed effects in the regressions), given that the micro studies do not tend to include other policy- and investment-specific controls. The results are very robust to these sensitivity checks: the coefficient on EPL is negative and is precisely estimated.

Table 8 Labour and product regulations, 1985–2013
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Other labour market indicators are also looked at. These are spending on active labour market polices, the tax wedge and the gross unemployment benefit replacement rate. ALMP is usually statistically significant (columns 2 and 4 in Table 8). Tax wedge and the gross unemployment benefit replacement rate either have large standard errors or have a counterintuitive positive sign (these results are not reported here). Therefore, these variables are dropped from further analysis.

5.3 Financial Development, Labour and Product Market Regulations

Access to finance is thought to be important for investment decision: a relatively easy availability to external funding is likely to increase investment. Three measures of external finance are used in this paper. One that approximates access to bank finance: the private credit to GDP ratio. Two other indicators used here measure market finance: stock market capitalisation over GDP; and stock market turnover over GDP. These finance indicators are added one-by-one to the specifications including product and labour market regulations. There is a fairly sizeable strong positive connection between capital stock and private credit as a share of GDP: a 1% increase in the private credit-to-GDP ratio is accompanied by a rise of 0.2% in the capital stock (column 1 in Table 9).

Table 9 Financial development & labour and product regulations, 1985–2013
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By contrast, it is more difficult to establish a statistically significant correlation between stock market capitalisation and turnover on the one hand and the capital stock on the other: the estimation results shed light on a small but positive relationship between the stock market variables and the capital stock. Yet this relationship becomes unstable to alternative model specifications, especially when these variables are used in levels (percentage points) rather than in log levels and when the capital stock-to-output ratio is used as the dependent variable.

The question one may want to ask now is what happens to the labour and product market regulation indicators. EPL, our labour market regulation indicator, comes across as an extremely robust variable in this new set of regressions. The inclusion of financial development does not change its significance, sign or magnitude: it has a negative sign and is significant at the 5% level in all cases. The size of the coefficient estimate is about 0.3, as before. The ETCR indicator, capturing product market regulation, also bears a strong negative relation to the capital stock, similarly to results reported in Tables 7 and 8.

5.4 Asymmetric Effects

Thus far, we have looked at simple linear relationships between the capital stock and structural policy indicators. Yet policies may bear a more complex relationship to investment. The relationship may be asymmetric to the direction of the change in policies, e.g. when policies are getting tighter or more competition friendly. Policies may amplify or attenuate each other’s influence on the capital stock. They may have a non-linear relationship to the capital stock.

Table 10 reports results of the analysis on directional asymmetries in the policy variables. Testing the null hypothesis of no asymmetry against the alternative of an asymmetric effect indicates the absence of directional asymmetry for the ETCR and private credit-to-GDP ratio. By contrast, the null of no asymmetry can be systematically rejected if asymmetry depends on directional changes in the EPL indicator (Table 10). The negative impact of ETCR and EPL on the capital stock is larger (and significant) if EPL is being increased, that is if employment protection legislation is becoming more stringent. At the same time, the positive correlation between private credit and the capital stock strengthens when EPL is being relaxed. But overall, these results are not robust when using the capital stock-to-output ratio (rather than the log real capital stock): the F- test cannot reject the null of parameter homogeneity (absence of asymmetric reaction). Also, the results for the private credit variable are sensitive whether this variable is considered in levels or in log-levels.

Table 10 Asymmetric effects, 1985–2013
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5.5 Smooth and Threshold non-linear Effects: Policy Effects Depending on their own Level

Policies may be related to investment through a long-term non-linear relationship. Two types of a possible non-linear relationship are considered here. First, squared terms of the policy indicators are added to the regressions. The squared term, if significant, implies a smooth non-linear effect. The estimation results shed light on a smooth non-linear effect of EPL on the capital stock (Table 11). Combining the coefficient estimates on the linear and squared term indicates that the negative correlation between EPL and the capital stock becomes smaller at lower levels of EPL. In policy terms, this implies that the payoff of relaxing employment protection legislation is larger if the initial level of protection is high.

Table 11 Smooth non-linear effects, 1985–2013
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Threshold regressions reported in Table 12 (columns 3 and 4) corroborate these results to some extent: the negative coefficient estimate on the EPL indicator becomes non-significant if EPL is below a certain level when using real capital stock. But this relationship breaks down for the capital stock/output is the dependent variable and when country averages of EPL are used as the threshold variable.

Table 12 Threshold non-linear effects, 1985–2013
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The empirical results show the absence of a smooth non-linear effect of ETCR and private credit: in alternative estimation setups, the coefficient estimates of these variables are estimated with high standard errors. Threshold regressions are also not very robust for these variables. For ETCR, whether the negative effect is larger or smaller when ETCR is high or low can change depending on model specification (Table 11).Footnote 10

5.6 Threshold non-linear Effects: Policy Effects Depending on the Level of Other Policies

Let us now turn to the threshold regressions in which the effects ETCR and EPL depend on the level of the PMR sub-indicators and the World Bank’s doing business and quality of institutions indicators, i.e. when the time-invariant variables are used as threshold variable. Generally speaking, ETCR appears to exhibit non-linear behaviour in function of the level of the headline PMR indicator: at higher levels of the overall PMR and its three main sub-components (state control, barriers to entrepreneurship; and barriers to trade and investment), the negative impact of ETCR on both measures of the capital stock are substantially larger (Table 12). This finding is in line with the threshold results when the country average of the ETCR indicator is used as a threshold variable. To illustrate the economic importance of this effect, if barriers to entrepreneurship is higher than 1.8, a one unit increase in ETCR will result in a 0.03% decrease in real capital stock and a 0.06 percentage point drop in the capital-to-output ratio. The threshold value of 1.8 is below the sample average of 2.06 (reported in Table 4). If this particular PMR sub-component is lower than 1.8, there is then no significant correlation between ETCR and the capital stock. There is a significant relationship for capital stock/output but the decrease is roughly two-third lower than in the higher regime.

The estimated threshold effects are very similar for EPL: EPL’s negative impact on capital is substantially higher if PMR is above the estimated threshold. The threshold values are surprisingly close to those estimated for ETCR. Also, these effects are in line with the results when country averages of ETCR are used as a threshold variable.

Looking now at threshold effects estimated for the doing business indicators, it is difficult to identify reasonably robust non-linear relationships for the impact of ETCR and EPL on the capital stock depending on the level of contract enforcement. For the various doing business indicators, whether or not the estimated effect in a particular non-linear regime is significant and whether the impact of ETCR and EPL is higher (lower) when the particular doing business indicator is above (below) the estimated tipping point depends on how capital stock is measured. In addition, similar measures, such as the cost and time of insolvency procedures yield contradicting results.

Finally, a straightforward pattern emerges for institutions: better rule of law and a higher quality legal system dampens the negative ETCR and EPL impacts. Indeed, if the rule of law and the quality of the legal system dampens the negative effect of EPL on the capital stock. ETCR has a negative effect on the capital stock-to-output ratio if the rule of law and the legal system do not attain a given level of quality. The estimated threshold effects are typically above the sample average

5.7 Policy Interactions

Looking at interactions with time-invariant structural characteristics provides useful insights on policy complementarities. The interactions for EPL and ETCR for which country averages of ETCR and EPL are interacted with time-varying EPL and ETCR series yield a fairly clear picture. The interaction terms are always negative. The base effects also tend to be strongly negative. This implies that countries with high level of ETCR will suffer from an overall higher negative ETCR impact. By the same token, countries with more stringent EPL will observe a more negative EPL impact. The combined effects of policies go in a similar direction. Higher ETCR exacerbates the negative impact of EPL. Also, higher EPL increases the negative ETCR impact.

Let us now turn to the interactions with the PMR indicator and its sub-components. The results are not very different from the average EPL and ETCR outcomes. A higher overall PMR indicator and higher levels of state control, barriers to entrepreneurship and larger barriers to trade and investment are all associated with a more negative ETCR and EPL impact on the capital stock.

The general business environment, captured through the World Bank’s doing business indicators do tend to provide with the fuzzy results observed for threshold regressions. One can observe both negative and positive interaction effects, with statistically non-significant results in a number of cases.

When it comes to institutions, they no doubt do matter for ETCR and EPL. Higher rule of law and better legal systems have consistently positive (and statistically significant) interaction terms. This means that countries with better institutions will face less negative ETCR and EPL impacts on their stock of capital. By contrast, in a country with weak rule of law, the negative ETCR and EPL effects will be larger (Tables 13 and 14). These results are very close to those reported from threshold regressions. Nevertheless, they differ in that the combination of the base and marginal effects may result in positive ETCR and EPL impacts if institutions are of high quality and that the negative overall ETCR and EPL effects can be more negative with very low-quality institutions.

Table 13 Policy interactions, 1985–2013
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Table 14 The impact of policies on the speed of adjustment, 1985–2013
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5.8 Policies, Institutions and the Speed of Adjustment

It is very tempting to assume that policies and institutions could have an influence on the speed of adjustment towards the long-run equilibrium. However, in practice and for our capital stock estimates, only two policies appear to affect the error correction term. They are the EPL and barriers to trade and investment. This suggests that countries with stricter EPL will experience a slower adjustment to the long-term equilibrium. But this also means that any reform that aims a lower EPL will speed up the convergence to the long-run steady state. By contrast, the marginal interaction term on barriers to trade and investment is negative. As the overall error correction term becomes more negative (larger in absolute terms), this means that countries with higher barriers and higher costs will reduce the gap to the long-run equilibrium at a higher speed. For instance, the impact of bad policies will materialise quicker.

6 Conclusion

This paper aimed to analyse the relationship between investment (capital stock) and structural policies including product and labour market regulation. Using a panel of 32 OECD countries for 1985 to 2013, our estimation results show that more stringent product and labour market regulations go hand in hand with a lower capital stock. An easier access to external finance attenuates the negative relationship between product and labour market policies and the capital stock.

We also provide strong empirical evidence for the existence of non-linear effects of EPL on the capital stock. Several alternative testing methods show that the negative influence of labour market regulations (EPL) is considerably higher at higher levels of EPL. The policy implications are that the payoffs of structural reforms are higher for countries with more stringent regulations and that the positive impact of labour market liberalisation declines once regulations are less biting.

Importantly, we shed light on important policy interactions. We made a strong case for interactions between product and labour market policies. We showed that all types of product market regulations (ranging from State control through barriers to entry & entrepreneurship to barriers to trade & investment) doubles the negative relationship that links EPL and the capital stock. Finally, our results indicate that the quality of institutions alters the overall impact of regulations on capital deepening: better insitutions reduces the negative effect of more stringent regulation on the capital stock, probably through the reduction of uncertaintly, so important for investment. These results have important policy implications. First, stringent regulations in product markets reinfiorce the negative effects of stringent labour market regulations (EPL). This implies that reforming EPL in countries with stricter product market regulations would have larger positive effects on investment. Second, countries with weaker insitutions could reap higher benefits from product and labour market reforms. This is probably because stringent regulations are more biting when weaker insitutions due to increase regulatory uncertainty regarding how complicated regulations will be enforced. Reducing the regulatory burden in such cases would boost investment morethan in countries with more effective law enforcement infrastructures.