Predicting US Recessions with Stock Market Illiquidity

Predicting US Recessions with Stock Market Illiquidity

∗Shiu-Sheng Chen† Yu-Hsi Chou‡ Chia-Yi Yen §

Abstract

In this paper, we investigate the dynamic link between recessions and stock

market liquidity by examining the predictive content of illiquidity for US recessions.

After controlling for other commonly featured recession predictors such as term

spreads and credit spreads, we find that the illiquidity measure proposed by Ami-

hud (2002) has strong power in predicting recessions. Moreover, the predictability

of the illiquidity measure of small firms is found to be stronger than that of large

firms, which supports the hypothesis of “flight to liquidity.”

Keywords: Recession; Stock market illiquidity; Probit model.

JEL Classification: E32, E44, G01.

∗We would like to thank two anonymous referees, and Chih-Yen Lin for helpful comments and sug-gestions.

†Department of Economics, National Taiwan University. E-mail: [email protected]‡Corresponding author. Department of Economics, Fu-Jen Catholic University, No.510, Zhongzheng

Rd., Xinzhuang Dist., New Taipei City, Taiwan. E-mail: [email protected], Tel: (+886)-2-2905-2709, Fax: (+886)-2-2905-2188.

§Quantitative Strategies Department, Risksoft Technology Ltd., Taipei City, Taiwan. E-mail:[email protected]

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1 Introduction

The stock market has long been viewed as a good leading indicator of real economic

activity. In particular, it is a common observation that stock market liquidity tends to

dry up as a precursor to recession (see Næs et al., 2011). As shown in McCracken (2010),

a chart combining a time-series plot of stock market liquidity with the National Bureau of

Economic Research (NBER) recession periods illustrates that liquidity tends to fall before

a recession and rise as the recession ends. A possible explanation is that stock market

liquidity may influence the real economy through the investment channel. For instance,

a liquid secondary market can facilitate the financing of long-run projects in economy

(Bencivenga et al., 1995; Levine and Zervos, 1998). Moreover, a liquid stock market may

lower the costs of raising external capital for firms (Levine, 1991). On the other hand,

even if there is no causal link between stock market liquidity and the recessions, a lead–lag

relationship between liquidity and recessions can be expected according to the “flight-to-

quality” phenomenon: when negative events about the economy that may cause future

recessions are expected (such as the bursting of a housing bubble), market participants

are likely to rebalance their portfolios toward less-risky assets (such as bonds) and away

from riskier assets (such as stocks), which lowers the liquidity of stock markets.

There are several studies investigating the link between stock market liquidity and

real economic activities. For instance, Levine and Zervos (1998) find significantly pos-

itive correlations between stock market liquidity and both current and future rates of

economic growth. Fujimoto (2004) and Soderberg (2009) investigate possible macroeco-

nomic sources of time-varying stock market liquidity. Finally, Næs et al. (2011) show

that changes in the US stock market liquidity have coincided with changes in the real

economy since World War II. Using the data of the US and Norway, they show that the

stock market liquidity measure is a good predictor of future changes of real gross domestic

product (GDP), unemployment, consumption and investment.

In this paper, we extend this body of work by examining the predictive content of

stock market illiquidity for recessions via in- and out-of-sample tests. As emphasized in

Estrella and Mishkin (1998), focusing on predicting recessions rather than on quantitative

measures of future economic activity (as in Næs et al., 2011) is a useful exercise because

whether a recession is going to take place is a question frequently posed by policy makers

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and market participants. To measure stock market illiquidity, we adopt the illiquidity

ratio proposed by Amihud (2002). The reason we use Amihud (2002)’s measure is twofold.

First, stock market liquidity usually means the ease of selling an asset in a short period

of time with minimal price impact, i.e., higher liquidity implies the price of an asset is

less affected when the transaction occurs. Thus, the measures of stock market liquidity in

the literature are in general related to transaction costs, trading volumes, and the ability

to capture price impacts. It is found in Goyenko and Trzcinka (2009) and Goyenko and

Ukhov (2009) that Amihud (2002)’s illiquidity measure does a better job in capturing price

impacts, while several liquidity measures proposed in the existing literature, including

those proposed by Lesmond et al. (1999), Roll (1984), and Amihud (2002), have been

compared. Second, Næs et al. (2011) show that Amihud (2002)’s illiquidity measure

outperforms other stock market liquidity measures in forecasting the growth rates of

GDP, consumption, and investment, especially in out-of-sample forecasting performance.

The closest study in spirit to the current analysis is that of Erdogan et al. (2014), which

constructs a leading indicator of recessions called macro liquidity deviation (MLD). The

MLD measure is obtained from the deviations from the normal statistical relationship

between a measure of stock market depth (ratio of the quarterly equity trading volume

to GDP) and a measure of stock market liquidity (ratio of the outstanding value of

listed securities to GDP). It is shown in Erdogan et al. (2014) that the MLD is able to

forecast future recessions. However, as a surprise deviation from normal equity market

liquidity relationships, while the MLD attempts to capture the “abnormal trading volume

increases,” it is not a genuine stock market liquidity measure. The MLD fails to reflect

certain features of liquidity such as transaction costs, trading volumes, and the ability to

capture price impacts.

We follow Kauppi and Saikkonen (2008) and Nyberg (2010) in considering both static

and dynamic probit models. Using US monthly data spanning from 1952M1 to 2011M12,

our empirical results suggest that Amihud (2002)’s illiquidity measure is a statistically

significant predictor of US recessions. Moreover, we find that combining Amihud (2002)’s

illiquidity measure with the classical recession predictors, such as term spreads and credit

spreads, provides a stronger forecasting performance for future recessions, both for in-

sample and out-of-sample tests.

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We also show that the sources of the predictive power of the illiquidity measure come

from the small firms rather than the large firms. This piece of evidence supports the

“flight-to-liquidity” hypothesis a la Longstaff (2004) in the US stock market. As a ro-

bustness check, we show that the strong predictive power of the illiquidity measure re-

mains when controlling some relevant variables, including aggregate stock returns, initial

public offering plus seasoned equity offering, and equity fund flows. Finally, the illiquid-

ity measure is also shown to be a significant leading indicator for future recession using

time-varying transition probabilities Markov-switching autoregressive models.

It is worth noting that our results show that the stock market illiquidity measure

is a powerful leading indicator for future recessions; however, preceding a recession and

actually causing a recession are two very different things. It is possible that a decline

in stock market liquidity itself did not cause the Great Recession, and the drying-up

of liquidity was simply a signal that something happened to economic fundamentals.

Although stock market illiquidity may not be a cause of recessions, monitoring stock

market liquidity as an early warning signal of future recessions is advisable. As it is

difficult to determine whether fundamental shifts are taking place in an economy, Amihud

(2002)’s stock market illiquidity measure is readily available in real time for forecasting

purposes.

This paper is organized as follows. Section 2 outlines our econometric framework

and Section 3 describes the data. Section 4 presents the empirical results, for both in-

sample and out-of-sample tests. Section 5 examines the predictive content of the illiquidity

measure for small firms and large firms. Section 6 provides robustness analysis, while

Section 7 concludes.

2 Econometric Framework

2.1 Stock Market Illiquidity Measure

Kyle (1985) and Brennan and Subrahmanyan (1996) attempt to measure stock market

liquidity by estimating how much prices move in response to trading volume. They define

the price impact as the response of prices to order flow. Amihud (2002) proposes a price

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impact measure to capture liquidity using daily trading data:

ILRi,t =1

Di,t

Di,t∑

d=1

|Ri,t,d|

V OLi,t,d

, (1)

where Di,t is the number of available trading days for stock i during period t. During

period t, |Ri,t,d| and V OLi,t,d are absolute returns and trading volume in dollars of stock i

during day d. That is, ILRi,t is calculated from the average ratio of absolute price changes

to trading volumes in dollars, which captures the daily price impact of the order flow.

Note that Amihud (2002)’s measure is called an illiquidity measure, as a high value of the

measure indicates low liquidity (high price impact of trades). That is, ILRi,t captures

how much the price moves for each volume unit of trades. After constructing ILRi,t, the

second step is to calculate the aggregated ILRt measure as an average market illiquidity

across stocks at a particular period t (for instance, month t):

ILRt =1

Nt

Nt∑

i=1

ILRi,t, (2)

where Nt is the number of stocks in period t. We then use the averaged stock market

illiquidity measure ILRt to predict future recessions. We follow Næs et al. (2011) in scaling

up ILRt by multiplying by 106 because the original magnitude of the ILRt measure is

too small to conduct a sensible empirical analysis. As the ILRt measure exhibits unit

roots, we follow Bouwman et al. (2012) to consider the annual change in log of ILRt for

monthly data as follows:1

dILRt = log ILRt − log ILRt−12.

2.2 Empirical Model

We define a recession indicator dt that characterizes the state of the economy as follows:

dt =

1 if the economy is in recession,

0 otherwise.

1We also follow Næs et al. (2011) to detrend ILRt using the Hodrick–Prescott filter, and obtain similarempirical results.

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Hence, conditional on the information set Ωt−1, the recession indicator dt has a Bernoulli

distribution with probability parameter pt, i.e., dt|Ωt−1 ∼ Bernoulli(pt). In order to

specify the conditional probability pt of a future recession, we consider a probit model in

which the conditional probability of the recession state dt = 1 satisfies:

pt = Et−1(dt) = Pt−1(dt = 1) = Φ(πt),

where Et−1[·] and Pt−1[·] denote the conditional expectation and probability, respectively,

and Φ(·) is the standard normal cumulative distribution function. To evaluate the pre-

dictive content of Amihud’s illiquidity ratio for recessions, we first consider a standard

static probit model that defines the term πt as:

πt ≡ α + βILRdILRt−k + γ′Xt−k, (3)

where dILRt−k is the annual change in stock market illiquidity in logarithms, and Xt−k is

the vector of explanatory variables containing classical recession predictors. Notice that

dILRt−k and Xt−k should satisfy the condition k ≥ h, where h is the forecast horizon.

An essential drawback of the static model in equation (3) is the lack of a dynamic

structure. We thus follow Dueker (1997), Kauppi and Saikkonen (2008), and Nyberg

(2010) to consider a natural extension to the static model by adding a lagged value of the

dependent time series dt−l to form a dynamic probit model:

πt ≡ α + βILRdILRt−k + γ′Xt−k + δdt−l, (4)

where l ≥ 1. Finally, we also consider one more interesting extension of the dynamic

model by including an interaction term:

πt ≡ α + βILRdILRt−k + γ′Xt−k + ω · (dt−l × dILRt−k). (5)

In equation (5), the impact of the illiquidity measure depends on the state of the econ-

omy, which enables us to investigate the possible state-dependent effect of the illiquidity

measure.

Equations (3) to (5) are estimated by the maximum likelihood method. The maximum

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likelihood estimate of θ for the vector of parameters θ = α, βILR, γ, δ, ω is found by

maximizing the following log-likelihood function:

logL(θ) =

T∑

t=1

[dt log(Φ(πt)) + (1− dt) log(1− Φ(πt))] . (6)

For the dynamic probit models (4) and (5), Estrella and Rodrigues (1998) and De Jong

and Woutersen (2011) show that under appropriate regularity conditions, the maximum

likelihood estimator θ is consistent and asymptotically normal. In particular, we follow

Kauppi and Saikkonen (2008) to calculate Newey–West-type robust standard errors.

To measure the model’s fit, we follow Estrella and Mishkin (1998) to compute the

pseudo-R2 developed by Estrella (1998):

Pseudo-R2 = 1−

(

logLu

logLc

)

−(2/T ) logLc

, (7)

where Lu denotes the value of the maximized probit likelihood, and Lc denotes the value

of the maximized likelihood under the constraint that all coefficients are zero except for

the constant. A low value of the pseudo-R2 suggests a “poor fit,” while pseudo-R2 = 1

represents a “perfect fit.”

We also make use of the receiver operating characteristics (ROC) curves, which eval-

uates the model’s ability to distinguish between recessions and non-recessions. The ROC

curve plots all possible combinations of true positive and false positive rates using thresh-

old values from 0 to 1. The ROC curve therefore plots the entire space of trade-offs

between correct and false recession signals as a function of the threshold used to make

classification based on a probability forecast. We report the area under the ROC curve

(AUC),2 which is a measure of the overall classification ability. A perfect recession clas-

sifier has an AUC of 1, whereas a coin-toss classifier has an AUC of 0.5.

Finally, we report the type I and type II errors, which present the average fraction of

periods that a recession is forecast when in fact no recession occurs and the average fraction

of periods that no recession is predicted when in fact a recession occurs, respectively. To

compute the type I and type II error, firstly we follow Youden (1950) to select the optimal

2The value of AUC is computed by trapezoidal approximation.

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cutoff threshold probabilities π∗ by maximizing the following objective function J :

argmaxπ

J = TP(π)− FP(π),

where TP(π) denotes the true positive rate, which is the average fraction of periods that

a recession is forecast when in fact recession occurs, and FP(π) is the false positive rate

that represents the average fraction of periods that a recession is forecast when in fact

no recession occurs. Hence, the optimal cutoff π∗ maximizes the capability of the model

to correctly discriminate between non-recession periods and recession periods. We then

compute the corresponding type I and type II errors given the optimal cutoff. Specifically:

Type I error =Total false alarms

Total non-recession periods= FP(π∗),

Type II error =Total missed recession periods

Total recession periods= 1− TP(π∗).

3 Data and Preliminary Test

In this paper, monthly data from 1952M1 to 2011M12 are used to examine the predictive

content of the illiquidity measure for recessions. The monthly aggregated illiquidity mea-

sure is constructed using data of individual stocks listed on the New York Stock Exchange

(NYSE). All the stocks have to meet the following requirements:

1. The stock must have more than 200 days’ trading in the last year to ensure more

stable estimates.

2. The stock price must be greater than $5 in the last trading day of the last year.

This enables us to exclude the noise of the estimates because a low-price stock can

be affected easily by the minimum tick.

3. The stock must have market capitalization data in the Center for Research in Se-

curity Prices (CRSP) database at the end of last year. As a result, some derivative

securities would be excluded.

4. A stock that satisfies the above condition would be excluded if it is an outlier, that

is, in the lowest (1 percent) or highest (99 percent) tails of the distribution of ILRi,t.

8

All the daily stock market data are obtained from the CRSP database, including prices

and trading volumes. The description of ILRt is listed in the first column of Table

1. The number of stocks satisfying the above four criteria varies over time, ranging

from 716 to 2223. Moreover, the mean of ILRt is larger in recession periods than non-

recession periods, which suggests that the stock market liquidity declines during economic

downturns. In the first panel of Figure 1, ILRt is plotted, with shaded areas indicating

the NBER recession periods. Clearly, the ILRt is closely related to the business booms

and depressions: a rapid increase in the illiquidity measure is generally accompanied by

a recession. Similar findings is found in dILRt, which is plotted in Figure 2.

We use the NBER recession dates to construct the recession variable dt. Table 2 lists

the monthly recession reference dates in our sample periods. There are ten recession

episodes over 1953–2009. The duration of each recession period varies substantially, from

a short duration of 6–8 months in the 1980, 1990–1991 and 2001 recessions to a medium

duration of 9–11 months in the 1953–1954, 1957–1958 and 1960–1961 recessions, and a

long duration of 16–18 months in the 1973–1975, 1981–1982 and 2007–2009 recessions.

We also consider other classical recession predictors including the term spread Termt

and the credit spread Credt as control variables. The term spread is constructed as the

difference between the long-term bond yield and the three-month Treasury bill rate, which

are obtained from Ibbotson’s Stocks, Bonds, Bills, and Inflation Yearbook, and the Federal

Reserve Economic Data (FRED) database provided by the Federal Reserve Bank of St.

Louis, respectively.3 Finally, we use Moody’s Baa- and Aaa-rated corporate bond rates

from the FRED database to construct the Baa minus Aaa spread, Credt.4

4 Empirical Results

4.1 In-Sample Results

The in-sample estimation results are presented in Table 3, 4, and 5, respectively. Following

Dueker (1997), we set k = l = h to evaluate the predictive performance of dILRt over

3They are available on Amit Goyal’s homepage: http://www.hec.unil.ch/agoyal/.4We apply Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) unit root tests to all data series

used, and report the results in a supplementary appendix. Clearly, the null hypothesis of a unit rootprocess can be rejected for all series.

9

different horizons.5 The in-sample predictive power is measured at horizons of h = 1, 3,

6, 9, and 12 months.

As for the in-sample results of the static model in equation (3), we report the coefficient

estimates, Newey–West corrected t-statistics, pseudo-R2, AUC, as well as Type I and II

errors in Table 3.6 We also report the pseudo-R2 and AUC for the model without dILRt,

and denote them as pseudo-R2ex.dILR and AUCex.dILR, respectively. The upper panel

investigates the predictive ability of dILRt by including only dILRt as the predictor. The

results show that dILRt has strong predictive power for the recessions. The middle and the

lower panel report the results using Xt−k = Termt−k and Xt−k = Termt−k, Credt−k

as additional control variables, respectively. It is clear that the predictive ability of dILRt

remains for all horizons we investigate after adding more controls. Moreover, comparing

the pseudo-R2 and AUC with the pseudo-R2ex.dILR and AUCex.dILR shows that the model’s

goodness-of-fit improved significantly when using dILRt as the forecasting variable.

It is worth noting that inTable 3, the sign of the estimates of βILR, γTerm, and γCred

generally accord with economic intuition. For instance, dILRt and Credt are positively

associated with future recessions, implying that an increase in stock market illiquidity

and default risk raises the likelihood of future recessions. On the other hand, Termt is

negatively correlated with future recessions, which suggests that when the supply of long-

term bonds increases because of an expected economic expansion in the future, long-term

bond yields will rise with a lower probability of future recessions.

Table 4 reports the results of the dynamic model in equation (4). Based on the

pseudo-R2, it is obvious that the statistical improvement compared with the static models

is significant, which is consistent with the findings in Kauppi and Saikkonen (2008) and

Nyberg (2010). Most importantly, the predictive power of stock market illiquidity remains

statistically significant. In addition, the type I and type II errors are reduced at h = 1 to

6, which ranges from 0.02 to 0.26. These results suggest that the model correctly predicts

over 70% of recession periods and non-recession periods.

Table 5 shows the results of the inclusion of interaction terms dt−h×dILRt−h to capture

5Kauppi and Saikkonen (2008) and Nyberg (2010) argue that although it has been common to selectk = l = h, the latest values of the predictive variables included in the information set at the time theforecasts are made are not necessarily the best ones in terms of predictive power. However, the goal ofthis paper is to evaluate the predictive power of ILRt over various horizons, rather than to select thebest predictive model.

6A Barlett kernel with a bandwidth of 4(T/100)2/9 is used for the Newey–West estimator.

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the possible asymmetric predictive power of stock market illiquidity for recessions. We

find that the coefficient estimates of the interaction terms are positive and statistically

significant at h = 1 and 3, for all specifications we consider. This result suggests that stock

market illiquidity predicts a higher recession probability when the economy is currently

in recession. This can be justified by a class of models with financial frictions and capital

market imperfections (see Bernanke and Gertler, 1989; Gertler, 1988, and the references

therein). In these models, the financing constraint is more likely to bind during economic

downturns; thus, an increase in stock market illiquidity in a recession will increase the

future probability of becoming trapped in a recession state.

In sum, the in-sample analysis shows that we are able to obtain much more informa-

tion about future recessions by using the stock market illiquidity measure as the leading

indicator, and the predictive content of the stock market illiquidity measure remains even

when controlling for the classical recession predictors such as term spreads and credit

spreads. Finally, there is evidence of asymmetry in the predictive power of the stock

market illiquidity ratio in predicting recessions across different economic states.

4.2 Out-of-Sample Forecasts

The in-sample evidence shows that the stock market illiquidity measure delivers good

predictability for recessions. However, it is well-known that good in-sample results do not

guarantee good out-of-sample predictability. Therefore, we conduct further out-of-sample

prediction exercises as in Estrella and Mishkin (1998). As we have found that the out-of-

sample forecasting performance of the dynamic probit model is substantially better than

static probit models, which is consistent with recent research (see Dueker, 1997; Kauppi

and Saikkonen, 2008; Ng, 2012; Nyberg, 2010, among others), we only report the results

of the dynamic probit model.7

In addition, the stock market illiquidity measure and other classical recession predic-

tors are available in real time; however, the NBER recession dates are announced with

substantial time delays. Thus, we need to take this practical issue into consideration and

make our assumptions based on what information is available at the time of making the

forecasts. As shown by Ng (2012), the average publication lag during 1980–2008 is about

7The out-of-sample test results for static models are available upon request.

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nine months. Thus, we follow Nyberg (2010) by assuming a nine-month publication lag in

the recession indicator. We then set the initial estimation period to be 1952M1–1989M3

and recursively estimate the probit model and calculate the h-step-ahead forecasts. The

out-of-sample forecasting period is from 1990M1 to 2011M3. Because of the assumed

delay in the publication of the recession indicator mentioned above, we focus on the cases

where h ≥ 10 and denote an “ahead” forecast horizon as hf , which is defined as hf = h−9

with h ≥ 10.

We apply the forecast method used by Estrella and Mishkin (1998) and Dueker (1997)

to construct out-of-sample forecasts. Specifically, using the law of iterated expectations,

the optimal h period forecast for dt based on information set Ωt−h = dt−h, dt−h−1, . . .,

dILRt−hf , dILRt−hf−1, . . ., xt−hf , xt−hf

−1, . . . has the conditional expectation:

Et−h(dt) = Et−h[Pt−1(dt = 1)] = Et−h[Φ(πt)]. (8)

Using the dynamic probit model in equation (4) as an illustration, the direct forecast for

the conditional probability in (8) at time t− h is given by:

Pt−1(dt = 1) = Φ(α + βILRdILRt−k + γ′Xt−k + δdt−l), (9)

and the conditions l = h, k = hf , and k ≥ 1 hold. The forecast based on equation (9)

gives a direct h-step-ahead forecast made at time t − h, so the forecast depends on only

the values of the recession indicator and the explanatory variables that are known at the

time of forecasting.

We consider forecast horizons hf = 1, 3, 6, 9, and 12 (so that h = 10, 12, 15, 18, and

21) because the publication lag is assumed to be nine months. To evaluate the out-

of-sample forecasting performance of the probit model, we use the pseudo-R2 and the

quadratic probability score (QPS) proposed by Diebold and Rudebusch (1989). Let T

denote the total number of sample observations, while R and P denote in- and out-of-

sample observations, respectively. The QPS can be calculated as follows:

QPS =1

P

T∑

t=R+1

2[Pt(dt+h = 1)− dt+h]2,

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where Pt(dt+h = 1) denotes the predictive value of the conditional probability of recessions.

Notice that the QPS ranges from 0 to 2, and QPS = 0 indicates that the probit model has

perfect predictive accuracy. Hence, a lower value of the QPS suggests better predictability

of the model.

We also report the out-of-sample pseudo-R2 as follows:

pseudo-R2OOS = 1−

(

logLOOSu

logLOOSc

)−(2/P ) logLOOSc

,

where logLOOSu denotes the value of the maximized probit likelihood using pseudo out-

of-sample observations, and LOOSc denotes the value of the out-of-sample constrained

maximized likelihood.

Table 6 presents the results from the out-of-sample forecasting exercise for the dynamic

probit models. According to the QPS, pseudo-R2OOS and AUC, we can observe that

dILRt remains a strong predictor of future recessions. For example, the pseudo-R2OOS for

the models with dILRt are 0.250 and 0.265 at hf = 9 for the model with dILRt, T ermt

and the model with dILRt, T ermt, Credt as predictive variables, respectively. In par-

ticular, the type II errors range from 0.029 to 0.294, which suggests that the dynamic

probit models successfully classify over 70% of the recession using out-of-sample forecast.

Overall, our empirical results show that the stock market illiquidity measure predicts the

future recession well in the out-of-sample forecast exercise, and supports the conclusions

drawn from the in-sample analysis.

To further highlight the predictive power of ILRt, we consider an out-of-sample fore-

casting exercise for predicting the 2007–2009 recession period with initial estimation peri-

ods from 1952M1 to 2005M12. Figure 3 illustrates the out-of-sample recession probabili-

ties from the beginning of 2006M1 with h = 10 (hf = 1) using the models with dILRt,

Termt, Credt and dILRt, T ermt, Credt as predictors, respectively. Clearly, the best

performance is obtained when considering dILRt in combination with the classical predic-

tors Termt and Credt, which successfully predicts the 2007–2009 financial crisis because

the recession probabilities forecast exceed the 50% threshold value in January 2008. On

the other hand, the model with Termt, Credt has weaker and delayed signals for the

recession periods. Figure 4 plots the results when h = 12 (hf = 3). The model with

Termt, Credt as explanatory variables fails to give precise recession signals as the re-

13

cession probabilities do not exceed 50% during the entire recession period, while the

model with dILRt and dILRt, T ermt, Credt deliver superior predictive ability for

the 2007–2009 crisis.

5 Firm-Size Effect

As shown in Næs et al. (2011), because small firms are relatively more sensitive to eco-

nomic downturns than large firms, it is more likely that an investor removes from his/her

portfolio those stocks with lower liquidity or higher risk when the economy is in a re-

cession, and the liquidity of small firms should decline substantially to reflect this effect.

Næs et al. (2011) subsequently confirms this “flight to liquidity” hypothesis by showing

that small firms’ liquidity has more predictive information than large firms’ liquidity.

In order to address this hypothesis, firstly we construct the ILR for small and large

firms, and denote them as ILRst and ILRl

t, respectively. We then estimate the following

dynamic probit model:

πt ≡ α + βILRs

dILRst−k + βILRl

dILRlt−k + γ′Xt−k + δdt−l, (10)

where dILRst and dILRl

t denote the annual changes of ILRst and ILRl

t in logarithms, and

βILRs

and βILRl

measure the impact of the stock market illiquidity for small and large

firms on recession probabilities, respectively. If the “flight to liquidity” effect exists, we

would expect βILRs

to be significantly positive, and greater than βILRl

.

To construct ILRst and ILRl

t, firms with lower market capitalization (below the lowest

25th percentile in the previous year) are defined as small firms. On the other hand, we

define a firm as being large when its market capitalization in the previous year falls to the

highest 25th percentile. The reason for using the market capitalization from the previous

year is to make sure that all the data are available when making a prediction. The second

and third columns of Table 1 list the descriptive statistics of small firms and large firms,

respectively. It is of no surprise that on average ILRlt is much smaller than ILRs

t , as

large-cap stocks are less illiquid. Moreover, the variation in ILRst is much larger than

that in ILRt and ILRlt. In the second and third panels of Figure 1, we plot the illiquidity

measures (ILRlt and ILRs

t ) with the NBER recession periods.

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Table 7 reports the in-sample and out-of-sample results from equation (10). We find

that the estimates of βILRs

are significant for all horizons we investigate. In contrast,

βILRl

are insignificant except at h = 9. We also report the pseudo-R2 for the models

that exclude dILRst and dILRl

t as predictors, which we denote as pseudo-R2ex.dILRs and

pseudo-R2ex.dILRl , respectively. It is clear that the model excluding dILRs

t may have a lower

goodness of fit than the model excluding dILRlt, which further confirms that the illiquidity

measure of small firms is more informative in predicting recessions than is the measure

of large firms. Similarly, the model excluding dILRst has lower out-of-sample predictive

power of future recessions than the model excluding dILRlt according to QPS, pseudo-R2

and AUC. Overall, our results strongly support the “flight to liquidity” hypothesis.

6 Robustness Checks

We present three robustness issues as follows. First, other than classical recession predic-

tors, we consider the annualized stock market returns Srett as an additional regressor to

examine if the predictive power of the stock market illiquidity measure remains. Second,

we control the variables related to investment channel and flight-to-quality hypothesis to

examine if the stock market illiquidity measure can provide the information about future

recessions beyond these variables. Finally, we use a Markov-switching model to investi-

gate whether stock market illiquidity affects the transition probabilities from expansions

to recessions.

6.1 Predictive Content Beyond the Stock Returns

The control variables in our benchmark analysis are the so-called classical recession pre-

dictors, including the term spread and credit spread. However, a fall in stock returns could

signal a weakening of the economic outlook to the extent that stock prices are forward-

looking, and the dividends may move together with the economic conditions. Moreover,

stock returns have been found to contain additional predictive power along with the term

spread in predicting economic recessions (see Estrella and Mishkin, 1998; Nyberg, 2014;

Sensier et al., 2004, and the references therein). For this reason, we include the annual-

ized monthly aggregate stock market returns as an additional control variable to capture

15

information from the financial markets.

We use the annualized CRSP value-weighted returns to proxy stock market returns.

The in-sample and out-of-sample prediction results are presented in Table 8. Clearly,

both the test results suggest that dILRt is still able to predict recessions at all horizons

we consider. Further, QPS, pseudo-R2 and AUC suggest that dILRt has additional

predictive content beyond the stock returns. One explanation for why liquidity seems to

be a better predictor than stock returns is that stock returns contain a more complex

mix of information that contaminates the signals from stock returns (Harvey, 1988).

Early empirical studies also found that stock price changes were only of limited use to

predict economic downturns (Stock and Watson, 2003). To sum up, our empirical findings

demonstrate that our benchmark results are robust when controlling for stock returns as

an additional predictor.

6.2 More on the Specific Channels of Predictability

The stock market illiquidity affects the real economy mainly through the investment

channel and “flight-to-quality” behavior among investors. However, as the stock market

illiquidity measure proposed by Amihud (2002) is constructed based on absolute stock

returns and trading volume in secondary market, it would be more straightforward to

use total proceeds of initial public offering (IPO) and seasoned equity offering (SEO) to

uncover the investment channel. Moreover, the algorithmic trading accounts for large

fraction of trading volume nowadays, which may affect the stock market liquidity sub-

stantially (Hendershott et al., 2011). Thus, it could be more appropriate to use the data

of equity fund flows to capture the “flight-to-quality” behavior among investors than use

Amihud (2002)’s illiquidity measure.

To address these issues, we consider a dynamic probit model with the total proceeds

of IPO plus SEO and equity fund flows as additional regressors to examine if dILRt still

contains predictive power beyond these two variables:

πt ≡ α + βILRdILRt−h + βTermTermt−h + βCredCredt−h

+ βIPOSEOIPOSEOt−h + βEqffEqfft−h + δdt−h, (11)

16

where IPOSEOt denotes the total proceeds of IPO plus SEO in logarithms, and Eqfft

denotes the monthly equity fund flows in billions of dollars.

We obtain the total proceeds of IPO plus SEO information in the U.S. from the Global

New Issues database provided by Thompson Financial’s Securities Data Corporation Plat-

inum. The total proceeds of IPO plus SEO in aggregate level is obtained by summing up

the proceeds of IPO and SEO for each firm. Moreover, we proxy the equity fund flows

by using the monthly flows of mutual fund investment on U.S. domestic equities from

the Investment Company Institute. The sample span of IPOSEOt and Eqfft is from

1984M1 to 2011M12.

Table 9 represents the estimation results of equation (11). First, it can be observed

that IPOSEOt has no predictability on future recessions except at h = 12, which suggests

that IPOSEOt has barely predictability on future recessions. On the other hand, Eqfft

has a significantly negative impact on future probabilities of recession from h = 1 to

9. The result thus provides some support for the “flight-to-quality” hypothesis that the

mutual funds are likely to withdraw from the stock market during economic downturns.

However, the recession predictability remains for all forecasting horizons we considered

when using dILRt as a predictor. To sum up, the stock market illiquidity measure still has

strong predictive content over future recessions even when we add predictors which are

thought to measure the investment and flight-to-quality channels more directly. Finally,

our finding also support the view of Hendershott et al. (2011) that the algorithmic trading

and stock market liquidity are positively related in general.

6.3 Markov-Switching Model

In this section, we use Markov-switching models to examine whether stock market illiq-

uidity affects the probability of a recession. As an alternative business cycle dating

method, Markov-switching models have been applied widely for business cycle analy-

sis since the seminal work by Hamilton (1989). As shown in the previous literature, a

two-state Markov-switching model well characterizes the switching of economic fluctua-

tions between expansions and contractions (for instance, see Filardo and Gordon, 1998;

Hamilton and Perez-Quiros, 1996; Lam, 2004; McConnell and Perez-Quiros, 2000, and

the references therein). To further examine the relationship between stock market illiq-

17

uidity and recessions, we consider a time-varying transition probability Markov-switching

autoregressive (TVTP-MS-AR(q)) model, which allows the transition probability to vary

over time as a function of stock market illiquidity.

Following Filardo (1994) and Durland and McCurdy (1994), we consider the following

two-state TVTP-MS-AR(q) model of industrial production growth, ∆yt:

φ(L)(∆yt − µSt) = ǫt, ǫt ∼ N(0, σ2), (12)

where φ(L) = 1 − φ1L − φ2L2 − · · · − φqL

q is a polynomial in the lag operator L, µSt

is the state-dependent mean, and σ2 is the variance of ǫt, respectively. The unobserved

state variable St is a latent dummy variable equal to either 0 or 1, indicating recessions

or expansions, respectively. The state variable St is assumed to follow a Markov process

with a TVTP matrix as follows:

P (t) =

p00t (Zt) p10t (Zt)

p01t (Zt) p11t (Zt),

(13)

where pijt (Zt) = P (st = i|st−1 = j, Zt), Zt represents the variables that may affect the

transition probabilities, and p00t (Zt) + p01t (Zt) = 1, p10t (Zt) + p11t (Zt) = 1. The TVTP

matrix in equation (13) guides the switch between the two different regimes over time,

and is assumed to vary with the evolution of stock market illiquidity and other control

variables. Specifically:

p00t (Zt) =exp(α00 + βILR

00 dILRt−1 + γ′

00Xt−1)

1 + exp(α00 + βILR00 dILRt−1 + γ′

00Xt−1),

p10t (Zt) =exp(α10 + βILR

10 dILRt−1 + γ′

10Xt−1)

1 + exp(α10 + βILR10 dILRt−1 + γ′

10Xt−1),

where Xt−1 = [Termt−1, Credt−1]′. Notice that p10t (Zt) is the probability of switching

from an expansion to a recession. If stock market illiquidity pushes the economy into a

recession, we expect to obtain βILR10 > 0. On the other hand, βILR

00 > 0 suggests that an

increase in illiquidity raises the probability of remaining in the recession state.

Table 10 reports the estimation results of a TVTP-MS-AR(q) model. The lag length

q is set to be 4 by the Akaike information criterion. At first, it can be observed that the

18

TVTP-MS-AR(4) identifies a regime with a positive mean industrial production growth

rate µ1 > 0, and a regime with a negative mean industrial production growth rate µ0 < 0.

The high-mean and low-mean states of output growth are labeled conventionally as ex-

pansions and recessions, respectively. That is, the TVTP-MS-AR(4) model has identified

well the fluctuations in the economy, as in the previous literature. We plot the one-period-

ahead predicted probabilities of the recession states in Figure 5. When greater than 0.5,

the predicted probability shows strong evidence that the economy was in the recession

regime. As a comparison, the plots also contain shaded areas that represent the recession

periods identified by the NBER. Clearly, the TVTP-MS-AR(4) model provides a fairly

good fit to the NBER recession data.

We now turn our attention to the effect of stock market illiquidity. It can be observed in

Table 10 that βILR10 is positive and statistically significant, which provides strong evidence

that an increase in stock market illiquidity increases the probability of switching from

an expansion to a recession. Furthermore, βILR00 is positive and statistically significant,

which implies that an increase in stock market illiquidity increases the probability of being

trapped in the recession state. It is worth noting that we find βILR00 > βILR

10 for all cases,

which implies that the impact of stock market illiquidity on the transition probabilities is

stronger when the economy is currently in recession. This finding is consistent with the

results from the probit model shown in Table 5.

6.4 Other Robustness Checks

For additional robustness checks, we also show that the strong predictive power of the

illiquidity measure remains when using quarterly data and an alternative measure of stock

market liquidity proposed by Pastor and Stambough (2003). Due to limited space, these

results are reported in a not-for-publication supplementary appendix.

7 Conclusion

In this paper, we examined whether it is worthwhile monitoring stock market illiquidity

when it comes to predicting recessions. We provided comprehensive empirical evidence

that stock market illiquidity has vast predictive content for US recessions in addition to

19

classical recession predictors such as term spreads and credit spreads, and the finding is

robust to different specifications. Finally, we find the stock market illiquidity measure

based on small firms has more predictive power for future recessions than the illiquidity

measure based on large firms, which supports the “flight-to-liquidity” hypothesis.

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22

Table 1: Descriptive statistics of ILR

ILRt ILRst ILRl

t

Mean 0.340 0.772 0.036Mean (in recession) 0.543 1.432 0.052Mean (in non-recession) 0.251 0.638 0.033Mean (annual changes) -0.080 -0.076 -0.112Mean (annual changes in recession) 0.392 0.422 0.179Mean (annual changes in non-recession) -0.176 -0.176 -0.170Median 0.170 0.430 0.015Std.dev 0.451 0.886 0.050Mean (1950 – 1960) 0.997 1.915 0.126Std.dev (1950 – 1960) 0.630 0.864 0.042Mean (1960 – 1970) 0.438 1.078 0.065Std.dev (1960 –1970) 0.230 0.634 0.022Mean (1970 – 1980) 0.501 1.313 0.039Std.dev (1970 –1980) 0.355 0.934 0.024Mean (1980 – 1990) 0.14 0.405 0.008Std.dev (1980 –1990) 0.076 0.208 0.006Mean (1990 – 2000) 0.071 0.211 0.003Std.dev (1990 –2000) 0.046 0.146 0.001Mean (2000 – 2010) 0.028 0.084 0.001Std.dev (2000 – 2010) 0.021 0.059 0.001No. of Sector 6566 3319 1697No. of Obs 1,061,538 262,900 262,723

Note: ILRt, ILRst , ILR

lt are illiquidity measures us-

ing data from all firms, small firms, and large firms,respectively. Std.dev denotes the standard deviation.

23

Table 2: Monthly recession reference dates for the US: 1952M1 to 2011M12

From peak To trough

1953M7 1954M51957M8 1958M41960M4 1961M21969M12 1970M111973M11 1975M31980M1 1980M71981M7 1982M111990M7 1991M32001M3 2001M112007M12 2009M6

Total recession periods Total non-recession periods

121 599

24

Table 3: Results from Static Probit model

Model: πt ≡ α+ βILRdILRt−h

h=1 h=3 h=6 h=9 h=12

βILR 1.385* 1.441* 1.162* 0.886* 0.618*t-ratio (5.368) (5.231) (4.944) (3.899) (3.042)

pseudo-R2 0.183 0.193 0.140 0.088 0.045pseudo-R2

ex.dILR 0.000 0.000 0.000 0.000 0.000AUC 0.810 0.818 0.782 0.741 0.672

AUCex.dILR 0.500 0.500 0.500 0.500 0.500Type I error 0.285 0.254 0.262 0.392 0.417Type II error 0.189 0.207 0.270 0.189 0.288

Model: πt ≡ α+ βILRdILRt−h + γTermTermt−h

h=1 h=3 h=6 h=9 h=12

βILR 1.378* 1.402* 1.139* 0.832* 0.471*t-ratio (5.321) (4.894) (4.867) (3.475) (2.090)γTerm -0.012 -0.211* -0.373* -0.529* -0.557*t-ratio (-0.129) (-2.390) (-4.067) (-4.133) (-4.342)

pseudo-R2 0.183 0.224 0.228 0.243 0.213pseudo-R2

ex.dILR 0.009 0.051 0.112 0.185 0.194AUC 0.810 0.846 0.850 0.853 0.841


Model: πt ≡ α+ βILRILRt−h + γTermTermt−h + γCredCredt−h

h=1 h=3 h=6 h=9 h=12

βILR 1.272* 1.262* 1.036* 0.767* 0.445*t-ratio (4.829) (4.600) (4.767) (3.298) (1.987)γTerm -0.109* -0.277* -0.406* -0.556* -0.567*t-ratio (-1.311) (-2.972) (-4.397) (-4.245) (-4.334)γCred 1.092* 0.787* 0.455* 0.326 0.186t-ratio (3.740) (2.838) (1.716) (1.137) (0.639)

pseudo-R2 0.266 0.269 0.243 0.250 0.215pseudo-R2

ex.dILR 0.128 0.135 0.151 0.201 0.198AUC 0.847 0.868 0.865 0.860 0.846


Note: The numbers in parentheses are t-ratios. * indicates significanceat the 10% level or above.

25

Table 4: Results from Dynamic Probit model

Model: πt ≡ α+ βILRdILRt−h + δdt−h

h=1 h=3 h=6 h=9 h=12

βILR 1.052* 0.971* 0.907* 0.920* 0.803*t-ratio (4.021) (3.695) (3.789) (3.640) (3.567)

δ 3.392* 2.123* 0.985* 0.128 -0.393t-ratio (19.211) (10.275) (3.808) (0.401) (-1.183)

pseudo-R2 0.687 0.386 0.151 0.074 0.044pseudo-R2

ex.dILR 0.672 0.359 0.102 0.010 0.001AUC 0.976 0.903 0.803 0.740 0.679


Model: πt ≡ α+ βILRdILRt−h + γTermTermt−h + δdt−h

h=1 h=3 h=6 h=9 h=12

βILR 0.894* 0.861* 0.779* 0.784* 0.620*t-ratio (3.707) (3.396) (3.417) (3.094) (2.740)γTerm -0.326* -0.473* -0.455* -0.561* -0.570*t-ratio (-4.209) (-4.693) (-4.597) (-4.336) (-4.410)

δ 3.736* 2.577* 1.206* 0.271 -0.369t-ratio (17.112) (9.916) (4.001) (0.701) (-0.863)

pseudo-R2 0.714 0.479 0.276 0.251 0.227pseudo-R2

ex.dILR 0.702 0.458 0.240 0.202 0.195AUC 0.983 0.947 0.889 0.853 0.845


Model: πt ≡ α+ βILRdILRt−h + γTermTermt−h + γCredCredt−h + δdt−h

h=1 h=3 h=6 h=9 h=12

βILR 0.883* 0.843* 0.764* 0.778* 0.637*t-ratio (3.578) (3.320) (3.404) (3.123) (2.870)γTerm -0.345* -0.488* -0.466* -0.578* -0.554*t-ratio (-4.047) (-4.622) (-4.644) (-4.346) (-4.390)γCred 0.325 0.247 0.231 0.335 0.332t-ratio (1.596) (1.001) (0.907) (1.172) (1.117)

δ 3.596* 2.459* 1.101* 0.130 -0.494t-ratio (17.774) (10.233) (3.928) (0.351) (-1.159)

pseudo-R2 0.718 0.482 0.280 0.257 0.231pseudo-R2

ex.dILR 0.705 0.461 0.243 0.208 0.201AUC 0.985 0.949 0.892 0.859 0.855



26

Table 5: Results from Probit model with Interaction Terms

Model: πt ≡ α+ βILRdILRt−h + ω · (dt−h × dILRt−h)

h=1 h=3 h=6 h=9 h=12

βILR 0.613* 0.717* 0.952* 1.108* 0.900*t-ratio (4.476) (3.684) (3.430) (3.598) (3.402)

ω 2.190* 2.228* 0.560 -0.595 -0.894*t-ratio (2.740) (2.748) (1.318) (-1.423) (-2.192)

pseudo-R2 0.264 0.271 0.146 0.096 0.062AUC 0.841 0.853 0.791 0.738 0.685

Type I error 0.094 0.076 0.224 0.353 0.285Type II error 0.234 0.297 0.288 0.225 0.414

Model: πt ≡ α+ βILRdILRt−h + γTermTermt−h

+ω · (dt−h × dILRt−h)

h=1 h=3 h=6 h=9 h=12

βILR 0.595* 0.583* 0.817* 0.992* 0.737*t-ratio (4.022) (3.048) (3.234) (3.301) (2.837)γTerm -0.026 -0.267* -0.393* -0.522* -0.552*t-ratio (-0.388) (-2.779) (-4.378) (-4.059) (-4.162)

ω 2.193* 2.451* 0.795* -0.422 -0.851*t-ratio (2.725) (2.602) (1.706) (-0.850) (-1.680)

pseudo-R2 0.265 0.313 0.240 0.247 0.225AUC 0.843 0.891 0.863 0.852 0.846


Model: πt ≡ α+ βILRdILRt−h + γTermTermt−h + γCredCredt−h

+ω · (dt−h × dILRt−h)

h=1 h=3 h=6 h=9 h=12

βILR 0.662* 0.616* 0.841* 1.023* 0.754*t-ratio (4.215) (3.407) (3.434) (3.367) (2.920)γTerm -0.094 -0.290* -0.411* -0.555* -0.569*t-ratio (-1.277) (-3.085) (-4.506) (-4.172) (-4.217)γCred 0.941* 0.471 0.354 0.471 0.359t-ratio (3.098) (1.527) (1.240) (1.561) (1.182)

ω 1.836* 2.060* 0.530 -0.716 -1.021*t-ratio (2.263) (2.209) (1.167) (-1.515) (-2.149)

pseudo-R2 0.319 0.326 0.248 0.259 0.232AUC 0.852 0.894 0.870 0.861 0.856



27

Table 6: Out-of-sample Results from Dynamic Probit model

Model: πt ≡ α+ βILRdILRt−hf + γTermTermt−hf + δdt−h

h = 10 h = 12 h = 15 h = 18 h = 21

hf = 1 hf = 3 hf = 6 hf = 9 hf = 12

QPS 0.166 0.189 0.207 0.198 0.186QPSex.dILR 0.239 0.246 0.231 0.205 0.187pseudo-R2

OOS 0.202 0.228 0.231 0.250 0.218pseudo-R2

OOS ex.dILR 0.011 0.050 0.114 0.195 0.202AUC 0.747 0.785 0.786 0.785 0.837


Model: πt ≡ α+ βILRdILRt−hf + γTermTermt−hf

+γCredCredt−hf + δdt−h

h = 10 h = 12 h = 15 h = 18 h = 21

hf = 1 hf = 3 hf = 6 hf = 9 hf = 12


OOS 0.274 0.283 0.261 0.265 0.225pseudo-R2

OOS ex.dILR 0.144 0.160 0.179 0.223 0.213AUC 0.788 0.828 0.828 0.808 0.848


28

Table 7: Results from the Dynamic Probit model: Classification based on Firm Size

In-Sample Results

Model: πt ≡ α+ βILRs

dILRst−h + βILRl

dILRlt−h

+γTermTermt−h + γCredCredt−h + δdt−h

h=1 h=3 h=6 h=9 h=12

βILRs0.936* 0.957* 1.116* 1.262* 0.947*

t-ratio (2.211) (2.212) (2.971) (3.706) (2.939)

βILRl

-0.170 -0.288 -0.625 -0.879* -0.650t-ratio (-0.316) (-0.534) (-1.376) (-2.066) (-1.336)pseudo-R2 0.731 0.499 0.292 0.263 0.235pseudo-R2

ex.dILRs 0.719 0.479 0.256 0.217 0.207pseudo-R2

ex.dILRl 0.731 0.498 0.285 0.251 0.228

AUC 0.984 0.950 0.899 0.870 0.859AUCex.dILRs 0.978 0.934 0.873 0.841 0.842AUCex.dILRl 0.985 0.948 0.893 0.858 0.854Type I error 0.021 0.094 0.219 0.215 0.258Type II error 0.081 0.144 0.108 0.207 0.153

Out-of-Sample Results

Model: πt ≡ α+ βILRs

dILRst−hf + βILRl

dILRlt−hf

+γTermTermt−hf + γCredCredt−hf + δdt−h

h = 10 h = 12 h = 15 h = 18 h = 21

hf = 1 hf = 3 hf = 6 hf = 9 hf = 12

QPS 0.139 0.165 0.197 0.190 0.187QPSex.dILRs 0.149 0.185 0.215 0.209 0.193QPSex.dILRl 0.135 0.162 0.196 0.197 0.186pseudo-R2

OOS 0.277 0.284 0.266 0.277 0.232pseudo-R2

OOS ex.dILRs 0.216 0.226 0.214 0.233 0.214pseudo-R2

OOS ex.dILRl 0.275 0.282 0.261 0.265 0.224

AUC 0.784 0.821 0.830 0.816 0.843AUCex.dILRs 0.759 0.769 0.769 0.764 0.815AUCex.dILRl 0.798 0.828 0.824 0.809 0.848Type I error 0.048 0.130 0.317 0.265 0.235Type II error 0.294 0.235 0.118 0.213 0.183


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Table 8: Results from Dynamic Probit Model with Stock Returns as Additional Regressor

In-Sample Results

Model: πt ≡ α+ βILRdILRt−h + γTermTermt−h + γCredCredt−h

+γSretSrett−h + δdt−h

h=1 h=3 h=6 h=9 h=12

βILR 0.774* 0.738* 0.690* 0.735* 0.599*t-ratio (3.096) (2.903) (3.037) (2.952) (2.706)γTerm -0.297* -0.465* -0.444* -0.557* -0.562*t-ratio (-3.412) (-4.529) (-4.627) (-4.273) (-4.251)γCred 0.307 0.170 0.174 0.365 0.436t-ratio (1.497) (0.716) (0.723) (1.286) (1.486)γSret -0.004* -0.004* -0.004* -0.002* -0.002*t-ratio (-2.285) (-3.188) (-3.116) (-2.822) (-2.559)

δ 3.672* 2.461* 0.971* -0.077 -0.712t-ratio (15.465) (9.278) (3.339) (-0.201) (-1.526)

Pseudo-R2 0.738 0.513 0.298 0.256 0.234pseudo-R2

ex.dILR 0.720 0.486 0.266 0.220 0.210AUC 0.983 0.951 0.896 0.864 0.857


Out-of-Sample Results

Model: πt ≡ α+ βILRdILRt−hf + γTermTermt−hf + γCredCredt−hf

+γSretSrett−hf + δdt−h

h = 10 h = 12 h = 15 h = 18 h = 21

hf = 1 hf = 3 hf = 6 hf = 9 hf = 12


OOS 0.277 0.295 0.277 0.271 0.228pseudo-R2

OOS ex.dILR 0.158 0.188 0.214 0.237 0.219AUC 0.789 0.829 0.853 0.812 0.851



30

Table 9: Results from Dynamic Probit Model with IPOSEOt and Eqfft as Additional Re-gressors

Model: πt ≡ α+ βILRdILRt−h + βTermTermt−h

+βCredCredt−h + βIPOSEOIPOSEOt−h + βEqffEqfft−h + δdt−h

h=1 h=3 h=6 h=9 h=12

βILR 1.951* 1.880* 1.820* 1.766* 2.031*t-ratio (2.324) (2.940) (3.146) (3.116) (2.922)γTerm -1.031* -0.861* -0.790* -0.981* -1.451*t-ratio (-2.462) (-4.207) (-3.711) (-3.803) (-6.520)γCred 1.245* 0.481 0.048 0.238 0.896*t-ratio (2.096) (1.135) (0.111) (0.468) (1.990)

γIPOSEO -0.053 -0.047 -0.065 0.083 0.225*t-ratio (-0.523) (-0.559) (-0.969) (0.933) (1.784)γEgff -0.065* -0.028 -0.029* -0.031* -0.011t-ratio (-3.352) (-1.633) (-1.850) (-2.004) (-0.724)

δ 5.359* 3.365* 2.130* 1.663* 1.844*t-ratio (5.210) (7.172) (3.840) (2.428) (2.996)

Pseudo-R2 [0.702] [0.464] [0.428] [0.280] [0.336]pseudo-R2

ex.dILR [0.674] [0.419] [0.253] [0.229] [0.275]AUC 0.994 0.968 0.931 0.917 0.930



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Table 10: Results from TVTP-MS-AR(4) Model

Zt = dILRt−1 Zt = dILRt−1, T ermt−1 Zt = dILRt−1, T ermt−1, Credt−1

µ0 -1.895* -1.984* -1.792*(-7.940) (-10.309) (-7.407)

µ1 0.427* 0.418* 0.490*(4.688) (5.630) (4.752)

φ1 0.195* 0.198* 0.215*(2.711) (4.095) (2.890)

φ2 0.153* 0.153* 0.163*(3.488) (3.676) (3.517)

φ3 0.194* 0.192* 0.207*(3.117) (3.901) (3.213)

φ4 0.072 0.076* 0.085(1.180) (1.689) (1.405)

log σ -0.326* -0.322* -0.333*(-4.682) (-10.975) (-4.688)

α00 0.461 1.462* 0.879(1.195) (1.851) (1.240)

α10 -3.995* -3.671* -5.247*(-12.549) (-8.136) (-4.374)

βILR00 2.199* 2.528* 1.287*

(2.047) (1.961) (1.692)βILR10 1.632* 1.460* 1.102*

(3.179) (2.489) (2.009)γTerm00 -0.624 -1.028*

(-1.449) (-2.427)γTerm10 -0.303 -0.589*

(-1.412) (-3.885)γCred00 1.451*

(2.129)γCred10 2.228*

(2.164)log-likelihood -861.08 -852.201 -850.718

Note: The numbers in parentheses are t-ratios. * indicates significance at the 10% levelor above.

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Figure 1: Plots of Amihud’s Monthly Illiquidity Measures. Shaded areas represent NBERrecession dates.

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Figure 2: Plots of Annual Changes in Illiquidity Measures. Shaded areas represent NBERrecession dates.

34

Figure 3: Out-of-sample Predicted Recession: one-month ahead. Shaded areas represent NBERrecession dates.

35

Figure 4: Out-of-sample Predicted Recession: three-month ahead. Shaded areas representNBER recession dates.

36

Figure 5: Plots of Predicted Recession Probabilities from TVTP-MS-AR(4) Model: one-monthahead. Shaded areas represent NBER recession dates.

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Predicting US Recessions with Stock Market Illiquidity

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