Time-varying Investment Dynamics in the USA

1 Introduction

The theoretical and empirical literature on aggregate investment has emphasized two features of utmost importance regarding its behavior: (i) that its dynamics are heavily influenced by Tobin’s q and cash flow; and (ii) that the investment sensitivities to both variables can vary dynamically and non-linearly over time.

First, aggregate investment is an increasing function of average Tobin’s q – the market valuation of a firm divided by the replacement cost of its capital stock – because this variable measures the average return on firms’ capital anticipated by the market, thus representing a proxy for the availability of external equity finance that influences firms’ investment expectations and decisions.

Second, aggregate investment is also an increasing function of cash flow since the latter captures the availability of internal funds, which are crucial for managing large and growing firms, as well as for financing new investment opportunities that firms deem potentially attractive.

Third, the relationship between investment, Tobin’s q, and cash flow does not seem to be static or stable over time because of the reasons associated with changes in adjustment costs, financial constraints, and technological improvements. This implies that dynamic non-linear models represent highly relevant avenues of research in order to provide a more comprehensive understanding of the behavior of aggregate investment over time.^[1]

In this article, we present the first study on the evolution of the time-varying sensitivities of aggregate investment to Tobin’s q and cash flow in the USA that considers a multiple equation model designed to capture time variation in the dynamic structural linkages among the variables as well as the possible time variation in the volatilities (heteroskedasticity) of the shocks. To do so, we estimate a time-varying parameter vector autoregression model with stochastic volatility (TVP-VAR-SV model) via Bayesian methods, along the lines of Del Negro and Primiceri (2015) and Primiceri (2005). Our empirical model (i) allows for a flexible strategy to study the possible time-varying behavior of the underlying structure of investment dynamics in a multivariate framework, (ii) allows for a structural interpretation of the dynamic responses of investment to changes in Tobin’s q and cash flow, and (iii) controls for the time-varying volatilities of the shocks over time.

Our main findings for the post-World War II period can be summarized as follows. First, we find significant evidence of time variation in the response of investment to shocks in Tobin’s q and cash flow, which highlights the existence of relevant structural changes in the dynamics of investment and its linkages to both variables.

Second, the time-varying response of investment to a shock to Tobin’s q is almost the mirror image to the time-varying response of investment to a shock to cash flow. Specifically, the time-varying sensitivity of investment to a shock in Tobin’s q decreased since the early 1960s through the early 1980s, increased since the early 1980s through the early 2000s, and it has tended to decrease importantly again since then. On the other hand, the time-varying sensitivity of investment to a shock in cash flow increased since the early 1960s through the early 1980s, decreased since the early 1980s through the early 2000s, and it has tended to increase importantly again since then. Such time-varying patterns in the investment sensitivities to Tobin’s q and cash flow are mainly observed in the short run, especially within the first 2 years after the initial shocks.

Hence, our results suggest that although Tobin’s q and cash flow represent complementary sources of information for investment dynamics because both variables influence simultaneously firms’ investment decisions, their relative importance for the latter has changed considerably over time, so that Tobin’s q and cash flow should also be regarded as alternative sources of information for short-run investment fluctuations.

The remainder of this article is organized as follows. A review of the literature that helps to motivate the current research is presented in Section 2. Section 3 presents the relevant data and discusses some stylized facts that additionally motivate the use of a TVP-VAR-SV model to study the dynamics of aggregate investment. The model and the empirical methodology are summarized in Section 4. Section 5 summarizes the main results, and, finally, the main conclusions are presented in Section 6.

2 Related Literature and Contribution

This contribution is mainly related to the theoretical and empirical literature that has emphasized that investment depends dynamically and non-linearly on variables associated with liquidity and finance constraints.

According to the original q theory of investment (Tobin, 1969), corporate investment is an increasing function of average Tobin’s q because, in equilibrium, the firms’ combined market value should be equal to their replacement costs – Tobin’s q ratio should be equal to 1 in equilibrium. A low Tobin’s q ratio – between 0 and 1 – can be regarded as an indicator that the cost to replace the firms’ assets is greater than the value of the stocks, so the stocks are undervalued. By contrast, a high Tobin’s q ratio – greater than 1 – can be considered as an indicator that the stocks are overvalued since the cost to replace the firms’ assets is lower than the value of the stocks. Therefore, Tobin’s q represents a variable that approximates the availability of external equity finance, which affects firms’ investment decisions mainly via investment expectations.

However, since Tobin’s q is an imperfect variable that regularly fails to control for the entire investment opportunity set, aggregate investment is also an increasing function of cash flow, i.e., a variable that captures the availability of internal funds. Different theories have been proposed to explain the positive relationship between investment decisions and cash flow, including the existence of agency problems (see, e.g., Grabowski & Mueller, 1972, among others) and asymmetric information (see, e.g., Stiglitz & Weiss, 1981, among others).^[2]

The existence of agency problems assumes that managers obtain financial and psychological gains from managing a large and growing firm, thus investing beyond the point that maximizes shareholder wealth. Although external capital sources could be used, internal funds are expected to be favored in this situation because they are the most accessible part of the capital market and are most malleable to managerial desires for growth. This also implies that a greater percentage of internal funds are retained and invested than are warranted to maximize shareholder welfare.

On the other hand, the existence of asymmetric information emphasizes that firms with attractive investment opportunities may be unable to finance their investment decisions because the cost of external funds can be too high due to the capital market’s ignorance of firms’ investment opportunities. If this occurs, firms with inadequate internal cash flows will not be able to finance their investment expenditures when needed; however, firms with large cash flows will be better prepared to finance their new investment opportunities.

In the same vein, the more recent theoretical models developed by Abel and Eberly (2011, 2012), and Lettau and Ludvigson (2002) articulate different possibilities to understand the simultaneous and potentially changing relationships between investment, Tobin’s q, and cash flow. To sum up, this strand of literature has shown three important results. First, there are significant dynamic interactions that can change over time between investment and Tobin’s q – for instance, because discount rates are not constant (Lettau & Ludvigson, 2002).

Second, even if other adjustment costs and financial constraints are eliminated, it can be shown that investment still remains sensitive to both Tobin’s q and cash flow (Abel & Eberly, 2011).

Third, when growth options that vary over time are considered – which occurs because the firm’s level of productivity is a choice variable, investment is positively correlated with cash flow during intervals of time between consecutive technology upgrades, but investment would be uncorrelated with Tobin’s q during such intervals. However, the positive correlation between investment and Tobin’s q is essentially associated with the forward-looking nature of the value of the firm, which can also change over time (Abel & Eberly, 2012).

At the empirical level, recent contributions have explored the possible changes over time of the sensitivity of investment to Tobin’s q and cash flow, mainly at the microlevel by considering firm-level data. Ağca and Mozumdar (2008), Brown and Petersen (2009), and Chen and Chen (2012) use US manufacturing firm data for the periods 1970–2001, 1970–2006, and 1967–2006, respectively. Ağca and Mozumdar (2008) controlled for other factors associated with capital market imperfections – namely, fund flows, institutional ownership, analyst following, bond ratings, and an index of antitakeover amendments, finding a steady decline in the estimated investment–cash flow sensitivity and a relatively stable investment-Tobin’s q sensitivity.

Brown and Petersen (2009) were mainly interested in studying how research and development (R&D) investment and developments in equity markets have impacted the investment–cash flow sensitivity, also finding an important decline of the latter over time and a smaller decline in the investment–Tobin’s q sensitivity.

Chen and Chen (2012) found that the investment–cash flow sensitivity declined over their entire sample period (and even completely disappeared during the 2007–2009 Great Financial Crisis); however, the investment–Tobin’s q sensitivity has remained relatively stable.

Likewise, Mclean and Zhao (2014) conducted their analysis using a sample of US firms for the period 1965–2010, showing that investment is more sensitive to Tobin’s q (cash flow) during expansions (recessions).

Both Grullon et al. (2018) and Lewellen and Lewellen (2002) emphasized the relevance of cash flow for investment decisions using a sample of US nonfinancial firms for the periods 1971–2009 and 1950–2011, respectively. However, while Lewellen and Lewellen (2002) suggested that this sensitivity has decreased, Grullon et al. (2018) found that the investment–cash flow sensitivity has increased for the largest 100 investing firms – which are the ones that explain approximately 60% of the total variation in aggregate investment.

Using quarterly aggregate data for the US economy, Gallegati and Ramsey (2013) and Verona (2020) employed wavelet analyses to study investment dynamics. Without considering cash flow, Gallegati and Ramsey (2013) found important evidence of instability regarding the investment–Tobin’s q relationship for the period 1952–2009, which even becomes negative during the 1980s. Verona (2020) considered the influence of both cash flow and Tobin’s q, finding that the investment–Tobin’s q sensitivity declined during the period 1952–2017, while the investment–cash flow sensitivity declined at business cycle frequencies but it tended to remain stable at lower frequencies (medium-to-long run).

The current article contributes to the aforementioned literature as follows. First, we focus on the analysis of investment dynamics at the aggregate level using a vector autoregression (VAR) model – a multiple equation modeling approach. Although microlevel studies and the use of firm-level data are important to capture the potential heterogeneity of investment decisions, for example, it is also challenging to capture the relevant dynamic interactions as well as the structural feedback effects between the variables of interest when using these methodologies. This helps to explain some of the considerably different results reported by this strand of literature.

Second, the incorporation of time-varying parameters (TVPs) into the VAR model represents a highly flexible non-linear framework for the estimation and interpretation of time variation in the systematic and non-systematic components of investment and its relationship to Tobin’s q and cash flow compared to rolling regressions, for example. The latter are widely employed by microlevel studies, but are known to lead to unreliable results in terms of spurious non-linear coefficient patterns.

Third, incorporating time-varying volatilities besides TVPs into the VAR model allows us to control for the possible time-varying heteroskedasticity of the shocks that have taken place during the post-World War II period – i.e., the Great Moderation. Thus, in our study, we model time-varying volatilities as stochastic volatilities (SVs), which allows us to provide a more comprehensive and robust characterization of the possible uncertainty around the estimates.

Thus, the TVP-VAR-SV model employed in this article to study aggregate investment complements directly the analysis of Verona (2020). Compared to the latter, our modeling approach captures only the short-run dynamic interactions between investment, Tobin’s q, and cash flow. However, we are able to provide a deeper understanding of the correlations discussed in his analysis – which are time-varying at different frequencies, but derived from a static investment equation that does not consider dynamic effects. By contrast, in our study, we are able to provide a time-varying structural interpretation of the dynamic interactions between the three variables that also controls for the time-varying volatility of the shocks.

Finally, our study also complements indirectly the recent contributions by Haque et al. (2021) and Mendieta-Muñoz & Sundal (2022). Haque et al. (2021) also used a TVP-VAR-SV model, but their interest consists in studying the effects of financial uncertainty shocks on investment, so they did not consider either the effects of Tobin’s q or cash flow in their empirical analysis. On the other hand, Mendieta-Muñoz & Sundal (2022) also studied some of the possible non-linear dynamic effects of investment, but they considered (i) a threshold VAR modeling approach instead of TVPs, thus focusing on threshold effects instead of time-variation as a potential source of non-linearity, and (ii) the effects of credit spreads instead of Tobin’s q.

3 Data and Stylized Facts

In order to focus on the interactions between the investment rate ( i t ), Tobin’s q ( q t ), and cash flow ( c t ), we used the same variables employed by Verona (2020). We considered quarterly time series data for the USA over the period 1951:Q4–2022:Q4, selected according to the availability of data. Figure 1 shows the time series plots of i t , q t and c t with National Bureau of Economic Research (NBER)-dated recession dates in shaded bars. The i t series corresponds to aggregate private non-residential fixed investment as a percentage of aggregate capital.^[3] The q t series corresponds to Tobin’s q of the nonfinancial corporate business sector, constructed as corporate equities as a percentage of net worth.^[4] The c t series is corporate profits as a percentage of gross domestic product (GDP).^[5]

Figure 1

USA, 1951:Q4–2022:Q4. Time series plots of Tobin’s q, cash flow, and investment rate. Shaded areas indicate the NBER recession dates.

From Figure 1, it is possible to observe that the procyclical i t has experienced substantial fluctuations over time. There have been two notable investment booms: the one starting in the early 1960s, which ended before the recession of 1969–70, and the one starting in the early 1990s, which ended just before the 2001 recession associated with the dot-com bubble. As also discussed by other contributions, investment has been declining since then, especially since the Great Financial Crisis of 2007–2009 (see, e.g., Gutiérrez & Phillippon, 2017).

During this period, the behavior of q t and c t has also changed considerably over time, which suggests that their respective effects on i t have been prima facie time-varying. Both variables exhibited relatively high levels before the 1970s, which coincides with the first investment boom, and declined up until the recession of 1990–1991 (although q t also rose since the early 1980s), which coincides with the trajectory of i t . However, q t is the only variable that experienced a clear sustained increase during the early 1990s, thus suggesting that the second boom in i t was mainly driven by this effect. Since the 2001 recession, both q t and c t have tended to show high levels – the only exceptions being during the global financial crisis of 2007–2009 and the coronavirus disease 2019 (COVID-19) recession of 2019–2020; however, i t has experienced lower levels.

To illustrate these points further, we provide a more detailed analysis for six different sub-periods – which, broadly speaking, try to capture the effects across different decades.

Table 1 presents some relevant descriptive statistics for the i t , q t , and c t series. We observe that the means (and medians) of the three series exhibit substantial variations since 1951:Q4 that strongly corroborate the description above. For instance, i t , q t , and c t presented relatively high means during the period 1951:Q4–1969:Q4 (approximately 3.6%, 111.3%, and 10.7%, respectively). Also, the lowest mean for i t corresponds to the period 2010:Q1–2022:Q4 (approximately 3.4%); however, q t and c t present their highest means (approximately 126.7% and 11.5%, respectively) during this period.

Importantly, Table 1 also shows that there have been considerable changes in the volatility of the three series across decades. The respective standard deviations show important evidence of time variation, especially the ones for q t and c t . This highlights that considering both SVs and TVPs is crucial to provide a more comprehensive and robust characterization of the dynamic interactions between the variables. As discussed in Section 2, in our study, we explicitly incorporate both SVs and TVPs by employing a TVP-VAR-SV modeling approach.^[6]

Figures 2 and 3 show the scatter plots between i t and q t and i t and c t , respectively. There is considerable heterogeneity regarding the interactions between the variables. For example, although the positive correlation between i t and q t is almost always corroborated, the association between these two variables is nonexistent during 1970:Q1–1979:Q4, this association is negative during 1980:Q1–1989:Q4, and the correlation also seems to be weak in the most recent period (2010:Q1–2022:Q4). Likewise, i t and c t seem to be positively correlated during most sub-periods; however, the association is negative during 2000:Q1–2009:Q4. There is also considerable variation regarding the constructed confidence intervals across the sub-periods, as shown in Figures 2 and 3, which suggests the important time variation with regard to the precision of the estimated effects.

Figure 2

USA, 1951:Q4–2022:Q4. Scatter plots between investment rate and Tobin’s q for different sub-periods. Straight lines show ordinary least squares (OLS) regression lines, assuming that all values of cash flow are fixed at zero. Shaded areas indicate 95% confidence level intervals of the regression lines.

Figure 3

USA, 1951:Q1–2022:Q4. Scatter plots between investment rate and cash flow for different sub-periods. Straight lines show OLS regression lines, assuming that all values of Tobin’s q are fixed at zero. Shaded areas indicate 95% confidence level intervals of the regression lines.

Finally, we summarize the response of i t to both q t and c t considering the different sub-periods via the regression analyses shown in Table 2. First, the results show that, overall, i t is more sensitive to c t than to q t . Second, the sensitivity of i t to both q t and c t has been different across the different sub-periods. For instance, the effect of c t on i t is statistically non-significant from 1990:Q1 through 2009:Q4, which corresponds to the two sub-periods where the largest statistically significant effects of q t on i t can be found.

The stylized facts presented in this section suggest that the dynamics of i t during the post-World War II period have been influenced by time-varying effects associated with both q t and c t . In other words, the sensitivity of i t to these two variables seems to be time-varying, so that the relevance of q t and c t for investment decisions has been changing over time. Moreover, the volatility of the series also seems to have changed substantially over time, so that the incorporation of time-varying volatilities into the modeling approach seems to be extremely relevant.

Motivated by this evidence, we use a TVP-VAR-SV model to formally study the interactions between the three variables and, most importantly, to capture the possible structural time-varying effects of both q t and c t on i t in a dynamic modeling framework that also controls for the possible time-varying volatility of the shocks.

4 Empirical Model

A reduced-form TVP-VAR-SV model of order p can be expressed as

where y t is an n X 1 vector of endogenous variables, C t is an n X 1 vector of intercepts, B p , t is an n X n matrix that contains the p th lag autoregressive coefficients, and u t are the heteroskedastic reduced-form shocks with time-varying variance–covariance matrix Ω t .

We can rewrite equation (1) as follows:

where X t ≡ I n ⊗ ( 1 , y t − 1 ′ , … , y t − P ′ ) , such that ⊗ denotes the Kronecker product; the vector β t is formed by stacking the elements of C t and B p , t equation by equation, so that β t ≡ vec ( [ C t , B 1 , t , … , B P , t ] ′ ) ; A t − 1 is a lower-triangular matrix with ones on the main diagonal and time-varying off-diagonal elements; Σ t is a time-varying diagonal matrix that contains the standard deviations of the structural shocks; and ε t ∼ N ( 0 , I n ) is the vector of standardized structural shocks, such that I n is an n -dimensional identity matrix.

Hence, as in Primiceri (2005), the model depicted by equation (2) incorporates two types of parameter instability: TVPs via β t (which captures the reduced-form coefficients) and A t − 1 (which captures the simultaneous relationships between the endogenous variables), as well as time-varying covariance terms via Σ t (which captures the SVs of structural shocks).

The dynamics of the model’s TVPs are specified as follows:

where α t = ( a 21 , t , … , a n n − 1 , t ) ′ is the vector of non-zero and non-unitary elements of A t (i.e., the lower-triangular elements of A t ) stacked by rows; σ t = ( σ 1 , t , … , σ n , t ) ′ is the vector of the main diagonal elements of Σ t Σ t ′ ; and { ν t , ζ t , η t } are i.i.d. Gaussian random shocks. Thus, equations (3)–(5) show that we assume that the parameters follow random walk processes – a flexible modeling assumption that allows us to capture both gradual and sudden structural changes.

Let us now define ψ = ( ε t , ν t , ζ t , η t ) ′ . Following Primiceri (2005), we assume that ψ ∼ N [ 0 , diag ( I n , Q , S , W ) ] , so ψ is jointly normally distributed with mutually uncorrelated white noise shocks, zero mean, and variances defined by I n and the hyper-parameters Q , S , and W , such that

where Q , S , and W are all diagonal positive semi-definite matrices that represent the variance–covariance matrices of shocks to β t , A t , and log σ t , respectively.

We rely on Markov chain Monte Carlo (MCMC) methods to estimate the TVP-VAR-SV model outlined earlier. First, we follow Primiceri (2005)’s sampling algorithm, but we modify the latter by incorporating the correction noted by Del Negro and Primiceri (2015). Second, we use the same prior distributions and initial states of the parameter distributions employed by Primiceri (2005).^[7] Third, using the relevant MCMC algorithm, we collect 205,000 posterior samples and discard the first 5,000 draws to ensure the convergence of the chain. Fourth, as in Primiceri (2005), we use p = 2 , so that we estimate the TVP-VAR-SV model considering two lags.^[8]

5 Summary of Findings

Our baseline results reported in this section consider the following ordering of variables to generate the impulse response functions (IRFs): y t = ( q t , c t , i t ) ′ . This implies that we order q t in y t first, c t second, and i t last.^[9] Hence, we assume that a shock in q t effects c t and i t contemporaneously; a shock to c t effects only i t within the same period; and i t does not effect c t and i t contemporaneously – it only does so with a lag. In short, this ordering of variables reflects that we believe that the availability of external equity finance approximated by q t is the most exogenous variable in the system since it is the variable that is most heavily influenced by expectations, followed by the availability of internal funds approximated by c t , while i t is the most endogenous variable in the system.^[10]

Figure 4

Posterior means of the standard deviations of residuals obtained from the TVP-VAR-SV model for the period 1961:Q4–2022:Q4. We report the time series plots of the means of the standard deviations of the residuals of Tobin’s q equation, cash flow equation, and investment rate equation in the TVP-VAR-SV model. Shaded areas show the 16th and 84th percentiles. Black horizontal lines show the means of the standard deviations of the residuals obtained from a standard VAR model (without TVP or SV) estimated via frequentist methods.

Figure 5

Time-varying response of investment rate to a shock in Tobin’s q at different quarters obtained from the TVP-VAR-SV model for the period 1961:Q4–2022:Q4. We report the time-varying median responses of the investment rate to a shock in Tobin’s q for different horizons. Shaded areas show the 16th and 84th percentiles: (a) within quarter (contemporaneous), (b) 1 quarter ahead, (c) 2 quarters ahead, (d) 3 quarters ahead, (e) 4 quarters ahead, (f) 8 quarters ahead, (g) 16 quarters ahead, and (h) 20 quarters ahead.

We begin by assessing the relevance of incorporating time-varying volatilities into the model by plotting the SVs aimed at capturing the heteroscedasticity of the shocks. Therefore, in Figure 4, we show the posterior mean together with the 16th and 84th percentiles of the time-varying standard deviation of the structural shocks. This is important to understand whether some variations in the dynamics in the model are associated with the variance–covariance matrix besides the TVPs in the model. We observe that the results indicate substantial time variation in the volatility of shocks. Specifically, Figure 4 shows that (i) the volatility of the shocks from the c t equation is the largest one; (ii) the volatilities of the shocks from the q t and c t equations are considerably more persistent than the volatility of the shocks from the i t equation; (iii) the volatility of the shocks from the q t equation has decreased over time; and (iv) the volatility of the shocks from the c t equation has slightly increased over time. This means that, besides TVPs in the VAR model, SVs are also important features of the dynamics of the system that need to be included as additional sources of time variation in the estimation.

Figure 6

Time-varying response of investment rate to a shock in cash flow at different quarters obtained from the TVP-VAR-SV model for the period 1961:Q4–2022:Q4. We report the time-varying median responses of the investment rate to a shock in cash flow for different horizons. Shaded areas show the 16th and 84th percentiles: (a) within quarter (contemporaneous), (b) 1 quarter ahead, (c) 2 quarters ahead, (d) 3 quarters ahead, (e) 4 quarters ahead, (f) 8 quarters ahead, (g) 16 quarters ahead, and (h) 20 quarters ahead.

Since our main interest consists in studying the possible time-varying effects of both q t and c t on i t , we focus on the responses of the latter to shocks in q t and c t . We summarize the time-varying sensitivity of i t to q t in Figure 5 by plotting the impulse responses over time at different quarters after the shock. In other words, we show the time-varying responses of i t to a shock in q t within the same quarter (contemporaneous effect), 1-quarter ahead, 2-quarters ahead, 3-quarters ahead, 4-quarters ahead, 8-quarters ahead, 16-quarters ahead, and 20-quarters ahead.

Figure 5  shows that a positive shock in q t increases i t during most quarters after the shock, since the great majority of the error bands do not enclose the zero line – the only exceptions being the time-varying contemporaneous effect (top-left figure), as well as the initial and final periods of the time-varying 1-quarter ahead response after the shock (top-right figure). Importantly, the sensitivity of i t to q t has changed considerably over time, mainly at 2, 3, 4, 8, 16, and 20 quarters after the shock in q t . To summarize, the sensitivity of i t to q t decreased since the early 1960s through the early 1980s, it increased since the early 1980s through the early 2000s, and it has decreased again since then. This is most clearly observed for the case of the time-varying response of i t after 2, 3, 4 and 8 quarters; however, the time-varying response of i t to a shock in q t after 16 and 20 quarters show a steady decline of this sensitivity during the period of study.

Regarding the possible changing nature of the effects of c t on i t , we summarize the time-varying sensitivity of i t to c t in Figure 6 by plotting the time-varying impulse responses of i t to a shock in c t within the same quarter (contemporaneous effect), and after 1 quarter, 2 quarters, 3 quarters, 4 quarters, 8 quarters, 16 quarters, and 20 quarters.

The results in Figure 6 show that most of the error bands do not enclose the zero line, thus indicating a strong positive response of i t to a shock in c t for the great majority of quarters after the shock – the only exception being the period between the late 1990s and early 2000s mainly for the time-varying contemporaneous effect (top-left figure) and one-quarter ahead response (top-right figure). Overall, compared to the responses of i t to q t , the responses of i t to c t in Figure 6 tend to be more persistent and of larger magnitude, which suggests that c t has played a more important role for investment decisions compared to q t over time.

Nevertheless, it is also clear that the response of i t to a shock in c t exhibits substantial time variation: it increased since the early 1960s through the early 1980s, it decreased since the early 1980s through the early 2000s, and it has tended to increase again since then. The latter is most clearly observed for the case of the time-varying response of i t to a shock in c t after one, two, three, four, and eight quarters; however, the 16- and 20-quarters ahead response of i t to c t show that this sensitivity remained relatively stable over time.^[11]

The main results can be summarized as follows. First, we find robust evidence of time-varying sensitivities of i t to shocks in both q t and c t . The time-varying response of i t to q t (Figure 5) decreased for the period 1960–1980, increased during the period 1980–2000, and decreased again for the period 2000–2022. The time-varying sensitivity of i t to c t (Figure 6) increased during the period 1960–1980, decreased for the period 1980–2000, and increased again during the period 1980–2022. These time-varying patterns are most strongly observed within the first 2 years (eight quarters) after the respective shocks, thus indicating that such changes in investment sensitivities mainly exist in the short-run.

Second, in the short-run, the evolution of the time-varying response of i t to a shock in c t is almost the mirror image to the evolution of the time-varying response of i t to a shock in q t . Importantly, this indicates that the two most important investment surges in the USA experienced during the late 1960s and early 2000s were associated with alternative sources: a higher sensitivity of i t to c t and a higher sensitivity of i t to q t , respectively.

Our empirical results corroborate the effects discussed by Abel and Eberly (2012) at the theoretical level, who showed that if growth options for firms are important and the firms’ productivity level is assumed to be endogenous (i.e., if it is assumed to be a choice variable), then i t depends more heavily on c t than on q t during periods of consecutive technology upgrades. In this sense, it is possible to say that the first investment surge in the late 1960s was associated with a higher sensitivity of i t to c t due to the consistent introduction of new technological improvements and higher productivity growth during this period. By contrast, the second investment surge in the early 2000s was associated with a higher sensitivity of i t to q t because of a more prominent role of expectations and the forward-looking behavior of firms, given the secular decline in technological progress growth rates experienced by the US economy.^[12]

6 Conclusions

What are the time-varying effects of the availability of external equity finance, approximated by Tobin’s q, and the availability of internal funds, approximated by cash flow, on the dynamics of aggregate investment? We answer this question for the post-World War II US economy by estimating a TVP-VAR-SV model via Bayesian methods.

We find new empirical evidence that contributes to our understanding of short-run fluctuations in investment. First, there is strong evidence showing that investment exhibits important time-varying sensitivities to both variables, thus indicating the existence of relevant structural changes in the dynamics of investment and its linkages to Tobin’s q and cash flow.

Second, the evolution of the time-varying sensitivity of investment to a shock to Tobin’s q decreased since the early 1960s through the early 1980s, increased since the early 1980s through the early 2000s, and it has decreased importantly again since then. By contrast, the time-varying sensitivity of investment to a shock to cash flow increased since the early 1960s through the early 1980s, decreased since the early 1980s through the early 2000s, and it has tended to increase importantly again since then. We find that these time-varying investment sensitivities are most strongly observed within a 2-year horizon, thus suggesting that these effects are mainly predominant in the short-run.

Hence, the short-run evolution of the time-varying response of investment to shocks to Tobin’s q is almost the mirror image to the short-run evolution of the time-varying response of investment to shocks to cash flow. These results indicate that although Tobin’s q and cash flow can be regarded as complementary sources of information for aggregate investment because both variables influence simultaneously firms’ investment decisions, the relative importance of each variable for investment fluctuations has changed considerably over time. This implies that both variables should also be regarded as alternative to each other in order to understand firms’ investment at the aggregate level in the short-run.

Future studies could fruitfully explore this finding further as follows. First, novel theoretical elements are needed to better understand the mechanisms that ultimately generate this phenomenon – by establishing a direct link between the relevant technological upgrades that may influence firms’ investment decisions to rely more heavily on cash flow or Tobin’s q during specific periods. Second, novel empirical research is also needed to identify the specific structural changes that shape the behavior of the TVPs and volatilities. This is work that remains to be done.