Private Debt, Public Debt, and Capital Misallocation

2.1 The Accumulation of Debt and Economic Outcomes

Over the last three decades, extensive research has been conducted on the relationship between private sector debt and economic growth. Earlier studies found positive effects of finance on growth (Beck et al., 2000; King & Levine, 1993; Levine et al., 2000; Rajan & Zingales, 1998). Huang and Lin (2009) find that financial intermediation has stronger growth-enhancing effects in low-income countries than in high-income countries; however, more recent studies have indicated that the effect of finance on growth is unlikely to be strictly positive. Shen and Lee (2006) show that the relationship between bank development and growth has an inverse U-shape in middle-income countries. Rousseau and Wachtel (2011) find that the positive finance–growth relationship, which was estimated using data from the 1960s to the 1980s, has disappeared over subsequent decades. Law and Singh (2014) estimate a threshold value of around 90–95% of GDP, beyond which financial development indicators (i.e., private sector credit and liquid liabilities) negatively affect growth. Arcand et al. (2015) find that financial depth has a negative effect on output growth when private sector credit reaches 100% of GDP. Mian et al. (2017) show that an increase in the household debt-to-GDP ratio predicts a lower subsequent GDP growth. Kobayashi and Shirai (2018) construct a theoretical model to show that excessive debt build-up in the private sector can depress economic growth through the persistent productive inefficiency of debt-ridden firms. Other studies document the detrimental effects of private credit growth on the financial stability and intensity of subsequent recessions (Jordà et al., 2011, 2013, 2015a; Mian & Sufi, 2010; Schularick & Taylor, 2012).

In addition to the growth effects of private sector debt, studies have analysed the relationship between public debt and economic growth since the publication of Reinhart and Rogoff’s (2009) seminal book. Reinhart and Rogoff (2010) find that in a sample of both advanced and emerging economies, public debt-to-GDP ratios as high as 90% and above are associated with significantly lower growth outcomes. While the results of Reinhart and Rogoff (2010) were famously criticized (Herndon et al., 2014), they also find support in other studies. For example, the findings of Cecchetti et al. (2011) suggest that in a sample of 18 OECD countries, increases in public debt beyond 85% of GDP have a negative effect on growth. Other articles confirming the nonlinear effects of public debt on growth include Baum et al. (2013), Checherita-Westphal and Rother (2012), Karadam (2018), Woo and Kumar (2015), and Yang and Su (2018). Chudik et al. (2017) find significant negative effects of public debt build-up on economic growth in the long run, although they find no evidence for a universally applicable threshold effect of public debt on growth. Panizza and Presbitero (2014), however, find no evidence for a causal effect of public debt on growth once corrected for endogeneity.

Other literature has focused on the joint dynamics of public and private debt. Reinhart and Rogoff (2011) document numerous episodes where surges in private debt before crises and surges in public debt after crises occur across advanced and emerging market economies. Reinhart et al. (2012) argue that there is a complex interaction between the different types of debt overhang and that the lines between public and private debt often become blurred in a crisis. After examining the co-evolution of public and private sector debt in 17 advanced countries over a 140-year period (1870–2011), Jordà et al. (2015b) show that financial stability risks primarily originate in the private rather than public sector; high public debt exacerbates the effects of private sector deleveraging after financial crises and hence contributes to deepening recessions following a credit bust. Research by Reinhart and Rogoff (2009) confirms these findings by showing that, in many crises over the past century, corporate defaults were precursors to government defaults or re-schedulings as governments tended to shoulder private sector debts. Figure 1 also shows that private debt in 18 EU countries had been rising for years preceding the 2007–2008 global financial crisis, while public debt has risen following the crisis. In a recent study using data from 29 OECD countries over 1995–2014, Caner et al. (2021) find that public and private debt stimulate economic growth at low levels of indebtedness but the interaction between these two types of debt decreases growth when the aggregate debt-to-GDP ratio reaches threshold level of 220%.

Figure 1

Time series of private and public debt (as % of GDP), average for 18 European countries. (Source: Author’s calculations based on IMF data).

Besides investigating the effects of debt on output growth, more recent research focuses on how debt accumulation impacts productivity and allocative efficiency. In one of the earlier articles, Kim and Maksimovic (1990) apply an econometric methodology for estimating the agency costs of debt to the air transport industry to show that high debt levels are associated with firm-level inefficiency and the fall in industry-wide productivity growth. Borio et al. (2015) study a sample of 21 OECD countries over 30 years and find that credit booms tend to undermine aggregate productivity growth, mainly through labour reallocations towards sectors with lower productivity growth. For a group of 20 OECD countries from 1970 to 2009, Salotti and Trecroci (2016) show that rising public debt levels are associated with lower rates of aggregate productivity growth. Using data regarding 20 advanced economies over 25 years, Cecchetti and Kharroubi (2019) argue that a country’s credit growth is a drag on its productivity growth, because credit booms slow growth in industries with lower asset tangibility or high research and development (R&D) intensity, which are usually regarded as engines for growth. Anderson and Raissi (2022) find significant negative effects of persistent corporate debt accumulation on the growth of TFP within Italian firms from 1999 to 2015. Kim et al. (2023) propose an accounting framework that maps the dispersion of borrowing costs along the debt maturity structure to the misallocation of productive resources, and they find that inefficient allocation of debt could reduce TFP by approximately 14.4% in the US manufacturing sector.

The TFP growth is the most important determinant of output growth in the long run (Caselli, 2005; Hall & Jones, 1999; Hsieh & Klenow, 2010; Klenow & Rodriguez-Clare, 1997), and this suggests that the observed differences in per capita income across countries are primarily due to the differences in their aggregate productivity. However, recent important research suggests that input misallocation – or the inefficient allocation of resources across firms and sectors – is a key factor in explaining differences in measured TFP. An article by Restuccia and Rogerson (2008) shows that policies distorting the prices faced by different producers lead to the reallocation of resources across productive units, thus entailing important effects on aggregate TFP. Hsieh and Klenow (2009) use microdata on manufacturing firms to document much higher dispersion of marginal products of capital and labour (i.e., measures of input misallocation) across plants in China and India compared to the United States. The authors also estimate large gains from reallocation: if the levels of dispersion in marginal products in China and India were counterfactually equalized to those in the U.S., TFP levels would be increased by 30–50% in China and 40–60% in India.

These studies suggest that aggregate productivity incorporates not only firm-level productive efficiency and industry-level technological advancement but also allocative efficiency across firms and industries. While some of the aforementioned research has examined how excessive leverage affects productivity outcomes, this article focuses specifically on how debt accumulation impacts capital allocation efficiency – an important economic phenomenon in its own right. The efficiency of capital allocation across firms has direct implications for investment returns, market competitiveness, and economic resilience. While determining the mechanism through which debt affects misallocation is more of a theoretical issue, this article investigates how increases in private and public debt influence capital misallocation depending on differences in industry characteristics. Understanding the relationship between debt accumulation and capital misallocation is important, as it sheds light on how financial systems interact with real economic activity.

2.2 Possible Relationship Between Debt and Misallocation

In addition to studies examining the effects of private and public debt on growth and productivity, an emerging body of research has also begun to investigate the relationship between debt accumulation and capital allocation efficiency. Aghion et al. (2019) develop a simple model to show an inverted-U relationship between credit access and aggregate productivity growth generated by two counteracting effects: (i) a positive investment effect of credit access on incumbent firms’ productivity growth through the facilitation of innovation, and (ii) a negative reallocation effect of credit access through the exit rate of incumbent firms and its influence on the entry cost for new – potentially more efficient – innovators. In a model of rational bubbles in the credit market, Pannella (2020) shows that high-credit periods allow larger but unproductive firms to increase their leverage compared to smaller and productive firms, thereby generating a misallocation of capital. Deng et al. (2023) find that the expansion of local government debt in China inhibits the efficient allocation of capital and increases urban carbon emissions. In a similar vein, Deng and Liu (2024) use city-level data from China to show that, out of different types of finance, one driven by local governments, particularly through land sales, exacerbates resource misallocation by directing funds to low-productivity state sectors. Using matched firm- and bank-level data for Spain, Basco et al. (2025) document that housing bubbles generate capital misallocation within industries and across municipalities by raising the value of the collateral disproportionately for firms and municipalities with greater real estate assets.

The above studies suggest that growing leverage in the financial sector could impact the efficiency of resource allocation in the economy. This association between debt and capital allocation efficiency is evident in Figure 2, where both private and public debt seem to positively correlate with capital misallocation (the country-level coefficients of correlation of capital misallocation with private debt and public debt, respectively, are 0.388 and 0.348).

Figure 2

Scatterplot of private/public debt and capital misallocation (Source: Author’s estimations based on the IMF and CompNet data. The estimations are at the country-year level, and MRPK dispersions are weighted averages, where the weights are country-specific time-varying sectoral value-added shares). (a) Private debt and capital misallocation. (b) Public debt and capital misallocation.

Recent studies reveal at least two main mechanisms or transmission channels through which debt accumulation at the aggregate level may affect capital misallocation across firms in a country or industry. The first is the existence of financial frictions and imperfections associated with pledgeable collateral or borrowing constraints. Moll (2014) argues that in a general equilibrium framework with borrowing constraints resulting from credit market imperfections, the equilibrium allocation implies that the marginal product of capital in highly productive firms exceeds that in less productive firms, unless idiosyncratic productivity shocks are persistent. Doerr (2020) similarly finds that rising property prices reduce aggregate productivity by reallocating capital and labour towards unproductive real estate owning firms. The second channel regards bubbles arising from excessive debt accumulation. Miao and Wang (2014) construct a two-sector endogenous growth model with credit-driven stock price bubbles to show that bubbles impact economic growth by easing access to credit and improving investment efficiency on the one hand, and by reallocating capital across sectors on the other. Basco et al. (2025) and Pannella (2020) also find distortionary effects of bubbles on capital allocation in the housing and credit markets. This article builds on insights from all these studies by examining how private debt accumulation interacts with sectoral characteristics to amplify capital misallocation.

In view of the discussion above, I hypothesize in this article that an increase in the supply of bank credit and other private debt instruments may exacerbate capital misallocation by disproportionately benefiting firms with easier access to credit (e.g., due to long-term relationships with banks) or better collateral (e.g., real estate assets). In such cases, an expansion of private lending should exacerbate capital misallocation disproportionately more in industries with greater inherent demand for external finance and higher average credit constraints or larger differences in credit constraints across firms. Regarding public debt, it is possible that an increase in public debt alters the allocation of capital by crowding out private credit (and directing funds to less productive state sectors) or subsidizing certain producers at the expense of others. In addition, other differences across firms (e.g., technological intensity or exposure to competition) could form the basis for the disproportionate effects of debt accumulation, leading to increased capital misallocation.

I adopt the framework developed by Hsieh and Klenow (2009) for the measurement of capital misallocation. Appendix A provides theoretical insight into capital misallocation and discusses its empirical measurement. It shows that the dispersion of marginal revenue products of capital and labour may reflect inefficiencies in resource allocation. While such inefficiencies may reduce aggregate productivity as discussed by Hsieh and Klenow (2009), this study focuses on understanding the effects of private debt on capital misallocation. My conjecture concerning the impact of aggregate debt on capital misallocation becomes justified if an increase in debt interacts with financial market frictions (e.g., differences in possession of real estate assets or access to credit) or other market imperfections in affecting the dispersion of the marginal revenue product of capital across firms. Therefore, the testable hypothesis of this article is that an increase in private and public debt accumulation in an economy with existing sectoral differences in terms of financial and technological constraints will exacerbate capital misallocation within sectors.

3.1 The Data

For capital misallocation, this study employs the 6th Vintage of CompNet database, which provides micro-based data regarding a range of indicators constructed on firm-level information, as described in Lopez-Garcia and Di Mauro (2015). The 6th Vintage of CompNet dataset represents an annual unbalanced panel covering 18 EU countries^[1] from 1999 to 2016, although data availability reduces this period to 2003–2015 for most of these countries. Indicators in the dataset were collected considering two samples of firms: those with at least one employee (the “full” sample) and those with at least 20 employees (the “20E” sample). In this analysis, I use the 20E sample since it is more homogenous and comparable across countries compared to the full sample, in particular due to exclusion rules in countries such as Poland and Slovakia, where only firms with more than 10 and 20 employees, respectively, must report their accounts. The dataset reports indicators aggregated at macro-sector (1-digit sectors corresponding to NACE Rev.2 sections) and sector (2-digit NACE Rev.2 sectors) levels. For each indicator in the 20E sample, firms are weighted according to their relative presence in the sample and are thus representative of the population of firms regarding sectoral distribution. I use the macro-sector-level data that include nine sectors of the economy at the one-digit industry level: manufacturing, construction, and seven service sectors (wholesale and retail trade; information and communication; transportation and storage; accommodation and food services; professional, scientific, and technical services; administrative and support services; real estate services).^[2]

I use the measure of capital misallocation defined, as in the seminal paper by Hsieh and Klenow (2009), as the dispersion of marginal revenue products of capital across firms within an industry. The intuition behind this definition is the following: under financial markets with no distortions, efficient within-industry allocation requires that marginal returns to capital across firms are equalized, since any firm with a higher return would have no difficulty in obtaining capital, hence bringing its marginal revenue product of capital down to the efficient level. Hsieh and Klenow (2009) show under some specific assumptions that an industry’s TFP is maximized when, other things equal, the dispersion of marginal revenue product of capital is zero. Therefore, the higher this dispersion, the higher is the misallocation of capital within the industry. However, capital misallocation defined this way is not necessarily comparable across industries and over time due to differences in adjustment costs and levels of uncertainty faced by firms in different industries (Asker et al., 2014). To address this issue, CompNet (6th Vintage) provides an adjusted measure of capital misallocation as proposed by Kehrig (2015).^[3] This is what I use as the dependent variable in my analysis.

The data concerning private and public debt originates from the International Monetary Fund’s Global Debt Database. Private debt comprises the total stock of loans and debt securities issued by households and nonfinancial corporations (as a share of GDP), while public debt consists of the total stock of debt liabilities issued by the general government (as a share of GDP). Control variables include the Chinn and Ito (2006) capital account openness index; long-term interest rates (OECD); general government final consumption expenditure (World Bank); taxes on income, profits, and capital gains (ICTD Government Revenue Dataset^[4]); trade (sum of exports and imports as a share of GDP, World Bank); sectoral average real turnover (CompNet); and an index of institutional quality measured as the sum of political risk rating indicators such as bureaucracy quality, investment profile, rule of law, and control of corruption (ICRG Researchers Dataset^[5]). The variables, such as private and public debt; government consumption; taxes on income, profits, and capital gains; and trade, are all in percent of GDP. The choice of control variables as possible determinants of capital misallocation is based on studies including Bai et al. (2019), Durnev (2010), Edmond et al. (2015), Gamberoni et al. (2016), Gopinath et al. (2017), Hassan et al. (2019), Larrain and Stumpner (2017), McNabb (2018), Monacelli and Sala (2018), and Ramey and Shapiro (1998). The explanatory variables are constructed as interaction terms between a time-varying country-level component and a time-invariant sectoral-level component (except for the average real turnover, which is available at the sectoral level from the CompNet database). Regarding sector-specific interacting variables, I use (i) an indicator of external finance dependence as in Rajan and Zingales (1998) – based on Compustat data on U.S. listed firms – obtained from Franco (2018); (ii) an indicator of credit constraints (ICC) available from CompNet database (i.e., share of credit constrained firms based on the methodology used in the survey on access to finance of enterprises, SAFE)^[6]; (iii) an indicator of sectoral technological intensity obtained from Eurostat (namely Eurostat indicators on high-tech industry and knowledge-intensive services).

Sector-specific interacting variables are used due to the absence of industry-level data concerning credit or debt ratios as well as the appeal of the difference-in-differences approach, which enables us to exploit the variation across industries to assess the impact of country-level variables on industry-level variables. Rajan and Zingales’ (1998) indicator is a commonly used measure of industries’ technological dependence on external finance. Because U.S. capital markets are “among the most advanced in the world, and large publicly traded firms typically face the least frictions in accessing finance” (Rajan & Zingales, 1998), the industry median of external finance dependence of large firms in the U.S. represents a useful measure of that industry’s inherent demand for external finance elsewhere. Regarding technological intensity, Calligaris et al. (2018) show that an increase in misallocation is positively correlated with R&D intensity at the sector level, and they argue that relative specialization in sectors where technology has been changing faster helps explain the patterns of misallocation across geographical areas and firm size classes. Cecchetti and Kharroubi (2019) also find negative effects of credit growth on TFP growth in sectors with high R&D intensity.

Appendix B, Table A2 provides the description and sources of data used in the analysis. The summary statistics of the variables are given in Table A3.

3.2 Preliminary Empirical Motivation

To contemplate the potential role of financial frictions in transmitting the effect of debt on capital misallocation, we can consider whether how well-established firms are in the market could be a plausible explanation for the differences in their financing constraints. Since I conjecture that borrowing constraints could be a factor that modulates the effect of debt on capital misallocation, evidence suggesting that longer-established firms face fewer such constraints could provide a hint for the transmission role of these constraints. To test the relationship between firm age and access-to-finance obstacles, I use a separate data source, where data are available from the World Bank’s Enterprise Surveys (WBES). The WBES provide firm-level data for more than 125,000 firms belonging to nearly fifty ISIC 2-digit business sectors in 146 countries, but I use the data for 26 EU countries (across several waves of the surveys)^[7] since the main analysis in this study concerns the EU countries only.

The WBES dataset has a variable measuring the degree to which access to finance is an obstacle to the firm’s current operations, and it ranges from 0 (no obstacle) to 4 (very severe obstacle). It can be seen from Table 1 that while more than 60% of firms that are older than 30 years report having no obstacle to access to finance, only 47.6% of firms that are younger than 10 years report having no such obstacle. While this seems to support my conjecture that older firms face fewer financing constraints, this cross-tabulation of access-to-finance obstacles and firm age does not control for unobserved country-specific and sector-specific heterogeneity. In order to address this, I run a regression of access-to-finance obstacles on firm age as well as firm size, controlling for country, sector, and survey-year fixed effects.

Table 2 demonstrates that older firms face fewer access-to-finance obstacles. It also shows that firm size is negatively correlated with these obstacles. This finding implies that, if younger (smaller) firms are more capital constrained (and hence have a higher marginal product of capital in general), then an increase in the supply of credit that disproportionately benefits older (larger) and less productive firms (due to the existing nature of financing obstacles or borrowing constraints) can widen the disparity of the marginal products of capital between the younger (smaller) and older (larger) firms. Although the substantive significance of the results in Table 2 is not high (the standardized versions of the coefficients for firm age and firm size are, respectively, −0.04 and −0.02), they still seem to support my basic premise that older (and larger) firms face fewer borrowing constraints than younger (and smaller) firms.

3.3 The Empirical Model

To examine the effects of private and public debt on capital misallocation, this study employs a difference-in-differences-type empirical methodology, whereby the aggregate (country-level) debt-to-GDP ratios are interacted with various sector-specific^[8] indicators, like the work of Larrain and Stumpner (2017) and Rajan and Zingales (1998). The empirical model appears as follows:

where Capital_Misallocation cjt denotes the level of capital misallocation for sector j in country c at time t, X ct is a vector of time-varying country-level controls, Z j is a sector-specific (time-invariant) indicator capturing industry-level characteristics, and φ cj is the country-sector fixed effects.

The empirical model uses the fixed-effects (within) regression since the explanatory variables of interest may be correlated with country and sector-specific unobserved factors. Standard errors are clustered at the country level; additionally, heteroscedasticity- and autocorrelation-consistent (HAC) standard errors are used as per Driscoll and Kraay (1998), which also addresses the potential cross-sectional dependence in the data (see Hoechle, 2007). For robustness, the model is tested using (the static version of) the generalized method of moments (GMM) system estimator developed by Arellano and Bond (1991), Arellano and Bover (1995), and Blundell and Bond (1998).

4.1 Baseline Regressions

This section discusses the results of the panel regressions. The explanatory variables include the natural logarithms of private debt, public debt, government consumption, taxes on income, profits and capital gains, trade, and sectoral average real turnover across firms,^[9] while also controlling for the long-term interest rate and indices for capital account openness^[10] and the quality of political institutions. The lagged values of the (logs of) private and public debt are used to account for potential endogeneity concerns, along with the lagged value of the capital account openness index – as in Larrain and Stumpner (2017) – since it is unlikely to have an immediate effect on capital misallocation.

Table 3 reports the results of fixed-effects regressions, where the explanatory variables are interacted with the sectoral-level indicator of external finance dependence. The results suggest that an increase in private debt exacerbates capital misallocation, and more so in sectors with higher financial dependence. While sectors that depend on external finance are more likely to benefit from higher credit availability, they also experience a larger increase in dispersion of marginal revenue products of capital following a rise in private sector indebtedness. To understand the size of the estimated effect, consider two (NACE 1-digit) sectors: one at the 75th percentile of the distribution of financial dependence (transportation and storage) and one at the 25th percentile (manufacturing). The difference in financial dependence between the two sectors is 0.11 (=0.40–0.29). A rise in private debt–to-GDP ratio by one standard deviation (i.e., 65.56 percentage points) is predicted to increase the dispersion in the return to capital in the sector at the 75th percentile of financial dependence by 0.457 more than in the sector at the 25th percentile (=0.994·ln(65.56)·0.11). This is equivalent to approximately 0.73 standard deviations of the dependent variable. Public debt, however, does not seem to affect capital misallocation after controlling for other potential determinants. The effect of capital account openness is found to be negative, meaning that financial liberalization reduces capital misallocation, supporting the findings of Larrain and Stumpner (2017). The coefficient of the long-term interest rate is also negative, suggesting that declining interest rates tend to increase the dispersion of returns to capital – which is supported by recent studies including Caggese and Pérez-Orive (2019), Cette et al. (2016), and Gopinath et al. (2017). No significant effect on capital misallocation of other control variables was found.

Table 4 reports the regression estimates, where the explanatory variables are interacted with the indicator of average credit constraints. The sign of the private debt coefficient is similar to that in Table 3: in sectors with a higher share of credit-constrained firms, a rise in private debt increases capital misallocation more than in sectors with a lower share of credit-constrained firms. To understand the magnitude of this effect, consider two country–sector pairs^[11]: one at the 75th percentile of the distribution of average credit constraints (information and communication in Italy) and one at the 25th percentile (administrative and support service activities in Croatia). The difference in the indicator of average credit constraints between the two country-sectors is 0.083 (=0.153–0.070). An increase in private debt by one standard deviation is predicted to increase the dispersion in the return to capital in the country-sector at the 75th percentile of average credit constraints by 1.177 units more than in the country-sector at the 25th percentile of the distribution (=3.389·ln(65.56)·0.083). This is equivalent to approximately 1.89 standard deviations of the dependent variable, which is not trivial. Although the coefficient of public debt is significantly positive in several columns that exclude most of the controls, it loses statistical significance when all controls are included. The long-term interest rate is found to improve capital allocation, as shown in Table 3, when the Driscoll-Kraay standard errors are used.

Table 5 shows the results of regressions where the explanatory variables are interacted with sectoral R&D intensity. The strong amplification effect of private debt is again confirmed: a rise in private debt increases capital misallocation, particularly in sectors that are more technologically intensive. A potential explanation is that R&D-intensive sectors are more likely to be credit constrained due to higher informational asymmetries, lower collateral value of firms (due to the elevated usage of intangible assets such as human capital and specialized machinery), and highly uncertain and skewed investment returns (Carpenter & Petersen, 2002; Fauceglia, 2015). To better understand the size of the effect, consider again two sectors: one at the 75th percentile of the distribution of technological intensity (transportation and storage) and one at the 25th percentile (e.g., construction). The difference in technological intensity between the two sectors is 0.402 (= 0.402 – 0). An increase in private debt-to-GDP ratio by one standard deviation is predicted to increase the dispersion in the return to capital in the sector at the 75th percentile of R&D intensity by 1.01 units more than in the sector at the 25th percentile (= 0.600·ln(65.56)·0.402). This is equivalent to approximately 1.62 standard deviations of capital misallocation. Public debt, again, has no significant capital misallocation effect at the 5% level of significance. The sign of the effect of financial openness is similar to that in Table 3, meaning that capital account liberalization may improve capital allocation (especially in highly R&D-intensive sectors), but there was no observed significant effect of interest rates in the current estimation.^[12]

Table 6 provides the results where capital misallocation is regressed on the two components of private debt separately: non-financial corporations’ debt and household debt. In these regressions, public debt is omitted since (i) its effect is insignificant and (ii) it does not noticeably increase the explanatory power of the regression model. The table shows that both corporate and household debt have significant amplifying effects on capital misallocation, but the effect of corporate debt is much larger (almost three times) than that of household debt. This finding is both intuitive and important since (i) capital misallocation is mainly the problem of the corporate sector, and (ii) this suggests that excessive corporate debt could be a more important factor in reallocating resources towards unproductive firms than household debt, which usually finances consumption rather than investment.

The observation of the much larger effect of corporate debt on capital misallocation than that of household debt warrants some discussion. Because corporate debt is more directly tied to business investment decisions, it is more likely to affect the allocation of capital among firms. On the contrary, household debt primarily finances consumption and housing, and hence may have only an indirect influence on resource misallocation across firms. Corporate debt directly affects firms’ capital structure, investment choices, and risk-taking behaviour. When corporate debt levels are high, financially constrained firms may face higher borrowing costs or credit rationing, while well-established firms with stronger banking relationships or better collateral may continue to access credit on favourable terms. This may widen the dispersion in marginal returns to capital across firms.

4.2 Robustness Tests

As a robustness check of the baseline specification, the regression model is estimated using the system GMM procedure proposed by Blundell and Bond (1998) – but without the autoregressive term^[13] – by instrumenting the explanatory variables with their lags, as described in Holtz-Eakin et al. (1988). To avoid the overfitting of endogenous variables and the associated bias caused by too many instruments, the instrument matrix is collapsed as recommended by Roodman (2009). Since the data are unbalanced and include gaps, instead of first differencing, forward orthogonal deviations are employed to transform the variables, as proposed by Arellano and Bover (1995). Standard errors are clustered at the country level.

Table A4 in the Appendix reports the one-step system GMM estimates using two instrument sets: all lags of the explanatory variables dated t – 2 and earlier, and those dated from t – 2 to t – 10. The results support the earlier finding that private debt accumulation increases capital misallocation, given the sectoral-level indicators such as financial dependence, average credit constraints, and R&D intensity, albeit the coefficients are statistically significant only at the 10% level in the case of the interaction with average credit constraints. Public debt, however, is found to have a somewhat negative effect on capital misallocation, particularly when the explanatory variables are interacted with financial dependence and technological intensity. The coefficients of private debt estimated with the GMM are noticeably smaller in magnitude than those estimated with the fixed effects estimator when the explanatory variables are interacted with the indicators of financial dependence and credit constraints, while the GMM-estimated coefficients are larger in magnitude when the explanatory variables are interacted with the indicator of technological intensity. All private debt coefficients estimated with the GMM, however, lie within the 95% confidence interval of those estimated with the fixed effects estimator. As before, negative coefficients are found for capital account openness and the long-term interest rate (where the coefficients on capital account openness are statistically significant only when using financial dependence and technological intensity as interacting variables, and the coefficients on the long-term interest rate are significant only when average credit constraints and technological intensity are used as interacting variables), which suggests that financial openness and higher interest rates tend to improve capital allocation. Moreover, demand conditions (proxied by average real turnover) are found to positively correlate with capital misallocation in some of the regressions, while the quality of political institutions seems to reduce capital misallocation in all interactions.

Table A5 in the Appendix presents the results of the robustness check – using both the fixed effects and the GMM estimators – excluding two countries, Germany and Spain, due to the small number of observations for the MRPK dispersion (Germany has 16 observations due to the data availability for the manufacturing sector only, and Spain has 56 observations since the data are available only starting from 2009). In addition, the data regarding credit constraints are not available for Hungary and the Slovak Republic for the regressions using the ICC as an interacting (sectoral-level) variable. The results in Table A5 show that the findings regarding the effect of private debt are robust to excluding certain countries from regressions.

In Table A6 in the Appendix, alternative sectoral-level indicators are used for interaction with the country-level explanatory variables. These indicators are available from the CompNet database at the sectoral level and were averaged over the available time period for each country-sector. In columns (1)–(3), the industry standard deviation of credit constraints (instead of the industry mean as performed earlier) is used to interact with the country-level variables. My hypothesis is that private debt may disproportionately increase capital misallocation in sectors with more heterogeneity in credit constraints. In columns (4)–(9), two measures of sectoral competitive structure are used as interacting variables: average markups (calculated as by De Loecker & Warzynski, 2012) and the skewness of sectoral TFP distribution.^[14] I conjecture that market imperfections such as the lack of competition could be the source of capital misallocation and that private debt may exacerbate this misallocation, particularly in sectors with a low level of competition (or a high level of concentration). The results in Table A6 support the hypothesis that private debt disproportionately increases capital misallocation in sectors with more heterogeneous credit constraints, higher average markups, and more skewed TFP distribution. Public debt is found to have no significant effect except in one regression, column (5), where it is found to increase capital misallocation when the Driscoll-Kraay standard errors are used. Capital account liberalization is found to have a significantly negative effect on capital misallocation when interacting with the skewness of TFP distribution, and the interest rate is found to have a significant negative effect when interacting with the dispersion of credit constraints.

Overall, the results suggest that excessive private debt accumulation is more detrimental to the efficiency of capital allocation across firms than public debt, because the latter entails no robust capital misallocation effect in this sample of European countries. The results further show that a rise in private debt disproportionately increases the dispersion of returns to capital in sectors that are, on average, more dependent on external finance, more credit-constrained, more technologically intensive, and less competitive. This confirms that continuous debt build-up in the private sector exacerbates capital misallocation by feeding on financial frictions, market imperfections, and existing differences across firms. The finding that higher long-term interest rates may reduce capital misallocation – particularly in sectors with higher financial dependence and credit constraints – strengthens this case since low interest rates are conducive to excessive debt accumulation. The results also confirm the finding of Larrain and Stumpner (2017) that capital account liberalization improves capital allocation in financially dependent industries, probably because this allows financially constrained domestic firms to access global capital markets, including foreign equity capital. An important finding of this article, however, is that private debt seems to be the most significant observable determinant of capital misallocation among all macroeconomic determinants used as explanatory variables in the panel regressions. This finding thus needs further exploration since it pertains to the economic effects of the financial sector that can destabilize entire economies.

To summarize, private debt accumulation in an economy with financial and technological constraints appears to deteriorate the efficiency of capital allocation, which is an important economic phenomenon with potential implications for investment and firm dynamics. The relationship between debt and capital misallocation deserves attention in its own right, as it directly affects how resources are distributed across firms and sectors. While the aggregate productivity effects of private debt accumulation exceed the scope of this article, it is significant that Aghion et al. (2019) find a two-sided effect of credit access on productivity growth, resulting in an inverted-U relationship. This leads to the conjecture that private debt might increase aggregate TFP at low levels of debt-to-GDP ratio by enabling firms to invest in new technologies, while high levels of private debt may reduce aggregate TFP growth due to its capital misallocation effect dominating the investment effect. Testing this conjecture, however, is left for future research.