### 1. Introduction

*informed*traders in the stock market, captures news shocks about future production growth more quickly than the movement of the total stock market index, such as the S&P 500 index examined in Beaudry and Portier (2006).

*uninformed*investors (i.e., noise traders) may also contribute to delayed stock price responses. Therefore, the total stock market index, which reflects the expectations of all types of investors, is less appropriate than the hedge fund index for capturing news about future economic conditions. In other words, if hedge fund managers are well-informed and have superior predictive skills, then the hedge fund index (i.e., aggregating the behaviors of informed traders) can be a more effective proxy for capturing agents’ expectations regarding future production growth. Recent studies examining hedge fund managers’ performance demonstrate their superior ability to identify mispricing in the stock market and gain an informational advantage in trading using various sources (Agarwal et al., 2009; Ben-David et al., 2012; Gao and Huang, 2016; Huang and Jain, 2024).

*TFP*).

*TFP*is the part of output that is unexplained by inputs for production, such as labor and capital.

*TFP*represents technological efficiency and explains economic growth (Easterly and Levine, 2001). Many studies empirically estimate country- or industry-level TFPs, but only annual frequency measures have been proposed because of data limitations. However, Fernald (2014) provides historical quarterly series of

*TFP*based on a growth-accounting database for the U.S. business sector. This study employs the Fernald’s quarterly

*TFP*series to measure productivity.

*TFP*and hedge fund index returns, this study examines the macroeconomic dynamics between hedge funds’ behaviors and economic productivity. The results are as follows. First, the contemporaneous correlation coefficient between the two variables is 0.9791, meaning that their movements are highly similar over the sample period. Note that the correlation coefficient between

*TFP*and a S&P500 Index is 0.6856.1) Second, a Granger Causality Test rejects the hypothesis, Δ

*Ln*(

*HFI*)does not Granger Cause Δ

*TFP*, implying that the information inferred from the behaviors of hedge funds seems to be useful to predict future economic productivity. Finally, the forecast error variance decompositions with the VECM model indicate that more than 65% of the variation in Δ

*TFP*after 20 quarters can be attributed to a shock to the Δ

*Ln*(

*HFI*).

### 2. Model Specification

### 2.1 Structural Vector Autoregressive Model (SVAR) and Impulse Responses

*y*is a (

_{t}*K*×1) vector of the endogenous variables,

*x*contains exogeneous variables, and the underlying structural shocks are

_{t}*ε*~ (0,

_{t}*I*). Matrix A specifies the instantaneous relations among the variables in

_{K}*y*, then the reduced-form disturbances are u

_{t}_{t}=

*A*

^{-1}

*Bε*. Using a Cholesky decomposition of the covariance matrix Σ

_{t}*and*

_{u}*B*to be a lower triangular matrix Σ

*=*

_{u}*BB*’’, I obtain the process

*y*=

_{t}*Φ*u

_{o}*+Φ*

_{t}_{1}u

*+… = Ψ*

_{t−1}*+Ψ*

_{o}ε_{t}_{1}

*ε*+…,, where Ψ

_{t−1}*= Φ*

_{i}*. I employ a long-run restriction on the SVAR following Blanchard and Quah (1989) and Beaudry and Portier (2006). Blanchard and Quah (1989) identify supply (demand) shocks with persistent (transitory) effects on output. Then, the (1,2)-element of the long-run impact matrix*

_{i}B*TFP*. Following Beaudry and Portier (2006), the estimation strategies of this study are in two ways, SVAR and VECM. First, the cointegration test with the Johansen method (allowing a linear trend in data and exogeneous variables) to examine whether a cointegration relationship exists between

*HFI*and

*TFP*level variables indicates no cointegration relationship between the two variables. However, for the first differenced variables, the cointegration test shows a statistically significant cointegration equation between the differenced endogenous variables. Thus, I employ the SVAR with the differenced variables and impose a restriction on the long-run impact matrix to observe the impulse responses of the shocks. Second, I adopt the VECM with differenced endogenous variables without restrictions as a robustness test.

*TFP*and

*HFI*. As deterministic terms, a constant term and a linear time trend term are included; and the HP-detrended stock market index,

*SNP500*, and the HP-detrended University of Michigan Consumer Sentiment Index,

*UM_SENT*, are also included as exogenous variables in the SVAR to compare the results with Beaudry and Portier (2006).2) Additionally, this allows me to identify the news shock inferred through the behavior of informed investors who expect better future production growth than the one observed by the behavior of all informed and uninformed stock market participants. I chose an optimal lag order of 1 for the main endogenous variables through the VAR lag-length test and include one-lagged detrended exogeneous variables.

##### <Table 1>

### 2.2 Vector Error Correction Models

*p*with a deterministic part given by

*μ*(typically, a polynomial in time) and a unmodeled stochastic or exogenous part,

_{t}*x*. One can write the

_{t}*n*-variate process

*y*. as

_{t}*n*, cointegration occurs and Π can be written as

*αβ*’. Then,

*β*is called a cointegrating vector and

*α*is called an adjustment vector. In this case,

*y*is I(1), but the combination (i.e., an error-correction term)

_{t}*ec*=

_{t}*β’y*is I(0). In fact,

_{t}*ec*represents the deviation from the long-run equilibrium relationship among the variables and may not be zero. The equation (3) is expressed as follows:

_{t}*β*is known, then

*ec*=

_{t-1}*β’y*would be observable and all the remaining parameters could be estimated via OLS (ordinary least squares). For example, if there are two endogenous variables with one cointegration relation, then

_{t-1}*TFP*and

*HFI*are described in <Table 1>. I include a constant and error correction terms as well as the HP-detrended stock market index,

*SNP500*, and the HP-detrended University of Michigan Consumer Sentiment Index,

*UM_SENT*, as exogenous variables in the VECM. I chose an optimal lag order of 1 for the main endogenous variables through the VAR lag-length test and include one-lagged detrended exogeneous variables.

### 3. Data Descriptions

### 3.1 Hedge Fund Industry

^{nd}quarter of 2023, according to the Barclay Hedge Fund database.3) The hedge fund industry fell significantly once in 2008, but the total AUM size has been continuously growing in recent days since the 2008 global financial crisis.

##### <Figure 1>

*informed*about future economic news than individual or noise investors. Therefore, the economic predictions by hedge fund managers can be considered more precise than those of other types of investors in the stock market. In addition, they are less regulated than other institutional investors (e.g., mutual fund) because many offshore centers provide business-friendly regulations for the hedge funds. Thus, the hedge fund index is a better proxy for the news shocks to future production or economic conditions than the stock market index, which reflects the expectations of all market participants.

### 3.2 Sample Construction and Summary Statistics

*TFP*series obtained from the Fernald’s website. The Credit Suisse/Tremont database, which tracks more than 9,000 funds, is used to determine the Index Universe. This selection universe is defined as only the funds with a minimum of $50 million under management, a minimum one-year track record, and current audited financial statements.6) The CSHF index is calculated with asset-weighting and rebalanced semi-annually. The index includes new funds using a rule-based construction method; therefore, it tracks at least the top 85% of the AUM in each of the 10 universe or strategy categories. The historical monthly indices from January 1994 to the present are available on the website.

*TFP*for the U.S. business sector. Shocks to quarterly estimated TFP are regarded as an important factor driving business cycle fluctuations (Kydland and Prescott, 1982). Because the

*TFP*series are only available at a quarterly frequency, I also use the CSHF index data from the end of each quarter. Therefore, the sample period for all the analyses is from the first quarter of 1994 to the second quarter of 2023 (118 observations).

*TFP*,

_{t}*HFI*), are employed as endogenous variables and the HP-detrended University of Michigan Consumer Sentiment Index and the HP-detrended stock market index, (

_{t}*UM*_

*SENT*,

_{t}*SNP*500

*), are included as exogenous variables. Barsky and Sims (2012) emphasize the importance of consumer confidence in forecasting future economic activity as confidence may reflect agents’ expectations of future economic productivity. Therefore, both the stock market index and consumer confidence survey results could also closely relate to future economic conditions.*

_{t}*TFP*series and business output series provided by Fernald (2014). Surprisingly, the hedge fund index (

*HFI*) and log-transformed TFP series (

*TFP*) show extremely similar patterns over the sample period. The correlation coefficient reported in <Table 2> between the two variables is 0.9791, implying that the behavior of

*informed*investors, such as hedge funds, is closely related to the productivity in the U.S. business sector.

##### <Table 2>

*TFP*and business output (

*Output*) is 0.9807, indicating that the difference in the various productivity measures is minor from an empirical perspective. The correlation coefficient between

*HFI*and

*TFP_Util*is also very high, at 0.9502. However, the correlation coefficient between

*SNP500*and

*TFP*is only 0.6598. Therefore, the stock market index seems to be much less related to the real economic productivity than the hedge fund index. If the stock market is somewhat informationally inefficient, then the stock prices reflect noisy information.

### 4. Empirical Results

##### <Table 3>

##### <Table 4>

Null Hypothesis: | Obs. | Chi-Sq. | d.f. | P-value |
---|---|---|---|---|

ΔLn(HFI) does not Granger Cause ΔTFP | 117 | 15.2379 | 1 | 0.0001 |

ΔTFP does not Granger Cause ΔLn(HFI) | 0.1827 | 1 | 0.6691 |

*TFP*, the t-statistics of one-quarter lagged Δ

*Ln*(

*HFI*) is 3.9036, meaning that the differenced hedge fund index is statistically significant to predict the current changes in TFP productivity. Moreover, the hedge fund index is statistically stronger than the contemporaneous and lagged

*SNP500*incorporating behaviors of all informed and uninformed investors. On the other hand, in the second column of <Table 3> predicting Δ

*Ln*(

*HFI*), the lagged Δ

*TFP*is not statistically significant to predict the current return or performance of the hedge fund index. The Granger Causality tests in <Table 4> also present results similar to those in <Table 3>, where the first null hypothesis is rejected, but the second null hypothesis cannot be rejected. Therefore, I conclude that informed investors, such as hedge funds, would recognize news shocks on economic productivity in advance and move faster than other market participants.

##### <Table 5>

*TFP*to a shock of Δ

*Ln*(

*HFI*) where the responses converge to zero regardless of imposing the long-run restriction in a year. That is, the effects of changes in hedge fund indexes on Δ

*TFP*are significant7) in the following quarter but almost disappear in 2 quarters after the shock of Δ

*Ln*(

*HFI*). Second, the lower-left panels present the effects of Δ

*TFP*shock on the returns in hedge fund indexes, Δ

*Ln*(

*HFI*). They appear insignificant even in the first quarter after the shock and gradually disappear within a year.

*TFP*is from shocks to the Δ

*Ln*(

*HFI*), and the contribution of Δ

*Ln*(

*HFI*)to the variation in Δ

*TFP*converges to 18.380% when a Structural decomposition method is employed. In the case of Δ

*Ln*(

*HFI*), approximately 13.341% of the variation in Δ

*Ln*(

*HFI*) is from shocks to Δ

*TFP*in the first period, and it converges to 13.904% and becomes stable after 3 quarters. Therefore, I conclude that hedge funds, as informed investors, would be able to know the news on future productivity in advance, so they move faster than any other agents in the economy.

^{st}differenced variables are cointegrated from the test. Following the literature, current and lagged

*UM_SENT*and

*SNP500*are also included as exogenous variables.

##### <Table 6>

*β*) and the adjustment vector (

*α*) are statistically significant, and represent the long-run equilibrium and short-run adjustment relationship between Δ(

*TFP)*and Δ

*Ln*(

*HFI*), respectively. In the first equation with a dependent variable Δ(Δ

*TFP*), the current and lagged stock market index,

*SNP500*and

*SNP500(-1)*are statistically significant although the lagged 2

^{nd}differenced hedge fund index, Δ(Δ

*Ln*(

*HFI*)), is not statistically significant, implying that stock market participants may capture well the future economic conditions in advance, so information from the stock market seems to be useful to expect future productivity. In the second equation with a dependent variable Δ(Δ

*Ln*(

*HFI*)), the current and lagged stock market index,

*SNP500*and

*SNP500(-1)*are also statistically significant, implying that the changes in performance of hedge funds are related to the stock market performance.

*TFP*to a shock of Δ

*Ln*(

*HFI*) where the responses converge to 1.1634 in a year. The magnitude of the impulse responses from 1

^{st}quarter to 2

^{nd}quarter is fairly large, at 1.5236, compared to the magnitudes of 0.8256 and 0.7932 from the SVAR model in <Table 5>. The lower-left panel of <Figure 5> shows the impulse response of Δ

*Ln*(

*HFI*) to a shock of Δ

*TFP*where the responses converge to 0.1034 in a year. The forecast error variance decompositions in <Table 7> also indicate that approximately 65% of the variation in Δ

*TFP*is from a shock to Δ

*Ln*(

*HFI*) in the horizon of 20 quarters, whereas approximately 18% of the variation in Δ

*Ln*(

*HFI*) is explained by a shock to the Δ

*TFP*.

##### <Table 7>

*informed*traders is more valuable for predicting future fundamentals or productivity than that inferred from the behaviors of all informed and uninformed traders. However, its predictive strength in the opposite direction appears to be limited.

### 5. Conclusions

*TFP*, and hedge funds’ behaviors,

*HFI*. The investment behaviors of hedge funds as

*informed*traders quickly capture the news shock about future production growth; therefore, the information inferred from the hedge fund index returns is useful for predicting future economic productivity or economic conditions. Using a quarterly series of

*TFP*and hedge fund index returns, this study finds that a predictive power exists in the behavior of hedge funds on real economic productivity. The findings from the SVAR and VECM models are robust regardless of whether a long-run restriction is imposed.