Predicting U.S. business cycles: an analysis based on credit spreads and market premium

Predicting U.S. business cycles: an analysis based

on credit spreads and market premium

Gabriel Koh, Aryo Baskoro, Riccardo Pianta, Si Qin

IB9X60 Quantitative Methods for Finance Group 10

List of Contents

Abstract .................................................................................................. 1

Introduction ............................................................................................. 1

Methodology ........................................................................................... 3

Time series model ................................................................................ 3

Stationarity ........................................................................................... 3

The probit model .................................................................................. 4

Maximum Likelihood Estimator ............................................................ 5

Partial Effect at the Average................................................................. 5

Relative partial effect............................................................................ 6

Pseudo-R2 ............................................................................................ 6

Likelihood-Ratio test............................................................................. 6

Data description ...................................................................................... 6

Empirical results ..................................................................................... 7

Test for stationarity .............................................................................. 7

Specifying the model ............................................................................ 7

Interpretation of results ......................................................................... 10

Caveats or limitations ............................................................................ 11

Conclusion ............................................................................................ 11

Bibliography .......................................................................................... 20


Abstract

Our paper aims to empirically test the significance of the credit spreads and excess returns of

the market portfolio in predicting the U.S. business cycles. We adopt the probit model to

estimate the partial effects of the variables using data from the Federal Reserve Economic

Data – St. Louis Fed (FRED) and the National Bureau of Economic Research (NBER) from

1993:12 to 2014:08. Results show that the contemporaneous regression model is not

significant while the predictive regression model is significant. Our tests show that only the

credit spread variable lagged by one period is significant and that the lagged variables of the

excess returns of the market portfolio is also significant. Therefore, we can conclude that credit

spreads and excess returns of the market portfolio can predict U.S. business cycles to a

certain extent.

Key words: Recessions, credit spreads, excess returns of the market portfolio (market

premium), probit models, U.S. business cycles

Introduction

After the most recent and influential business cycles fluctuations and financial crisis (especially

the one of 2008, widely known as ‘Sub Prime Mortgage Crisis’), many researchers put effort

to analyse and understand those variables that can explain recessions. There has been a rich

discussion on the impact of macroeconomic variables that determines the business cycle

fluctuations in the U.S. This research paper has been built upon a broad range of past literature

based on the usage of macroeconomic and financial variables to evaluate and estimate the

probability of recessions.

Estrella and Hardouvelis (1991) and Estrella and Mishkin (1998) have argued that the slope

of the term structure of Treasury yields has strong predictive power for forecasting U.S. cycles.

We use in our research the papers of Estrella and Hardouvelis (1991), being the first to advert

the Treasury term spread as a predictor of recessions. Per their findings, the treasury term

spread has greater explanatory power than a selected benchmark index. Following the

findings of Estrella and Hardouvelis (1991), using a similar research framework, Estrella and

Mishkin (1998) concluded the yield curve spread and the stock price index being the most

useful financial indicators to forecast recessions. Furthermore, by using the probit model,

Dueker (1997) found that the term spread represents the best recession indicator and

exhibited that the results are robust with lagged dependent variables. Chauvet and Potter

(2005) paper reveals that, otherwise it is difficult to predict recession, they managed to


construct the probabilities of recession of 2001 by using the probit model that includes the

term structure as a regressor. The outcome of their research is that under the presence of

structural break in a time series could considerably affect recession predictions.

Similarly, we find similar analysis conducted in the European regions, such as France and

Germany, to predict their recession: for instance, both Bismans and Majetti (2012) in France

and Nyberg (2010) in Germany used equivalent approach and adopting the probit model.

Consistent with most the previous past literature, we decided to employ binary response

variables to predict the business cycle fluctuation across time. On the other hand, empirical

studies have been conducted to thoroughly analyse the relationship between credit spread

and economic downturns. For instance, Gilchrist and Zakrajsek (2012) and Faust et al. (2013)

discovered the significance predictive abilities of credit spread on recessions, related to

business cycles.

We ask two primary questions in our research. First, we want to investigate any relationship

between the credit spreads and excess returns of the market portfolio on the probability of a

recessions and whether it is contemporaneous or predictive in nature. Secondly, we want to

determine the sign of lagged variables to ensure that the variables followed economic theory.

Our paper assesses the significance of credit spreads and the excess returns on the market

portfolio (market premium) on predicting business cycle fluctuations in the U.S. from 1993:12

to 2014:08 which merely includes two recessions.

In accordance with many of the prior researches, we extract the U.S recession data from the

Federal Reserve Economic Data – St. Louis Fed (FRED) and the National Bureau of Economic

Research (NBER) for our analysis. This variable is binary; a value of 1 represents a

recessionary period, while a value of 0 represents an expansionary period. In our set of data,

the recession begins from the first day of the period following a peak and ends on the day of

the period of the trough. On the contrary, our leading financial indicators have continuous

distributions.

Given the characteristics of our data, we adopt the probit model following previous literature

to estimate the explanatory variables. We proceed determining the credit spread as the

difference between the Baa Moodys and the Aaa Moodys and the excess return of the market

portfolio as the difference between the value weighted market portfolio and the risk-free rate,

as defined by Bianchi, Guidolin and Ravazzolo (2013).

In general, we would expect that there would be a positive relationship between the credit

spread and the likelihood of a recession and a negative relationship between the excess

returns of the market portfolio and the likelihood of a recession.


Having recognised that the model is a time series, we conduct a unit root testing following the

methodology footsteps of Karunaratne (2002). We begin testing the stationarity of the

independent variables (credit spread and excess returns of the market portfolio) to ensure that

the regression is not spurious (Granger & Newbold, 1973). We run the Dickey-Fuller test for

unit root and the Augmented Dickey-Fuller test for unit root to confirm that these variables are

stationary (see Dickey & Fuller, 1979).

We have examined the contemporaneous regression model where we estimate the effects of

the current credit spreads and the excess returns of the market portfolio on the probability of

a recession in that period. Intuitively, given that the data in the current period is unobservable,

we should not find any significance in the contemporaneous regression model.

Instead, a predictive regression model would be much more appropriate. We proceed by

estimating the effects of the lagged credit spreads and the excess returns of the market

portfolio on the probability of a recession. We start by estimating the probit model on a single

lag of each variable and continue adding further lagged variables until we find an insignificant

lag.

Methodology

In the following chapter, we describe the empirical methods that we use to estimate the

significance of financial indicators in determining U.S. business cycles. First, we will start by

discussing the time series model as well as the need to test the stationarity of variables to

avoid the presence of spurious regressions that may lead to misleading inferences. Next, we

describe the conventions of the probit model and its advantages along with the maximum

likelihood estimator. Lastly, we address the interpretation of results and goodness of fit

measures.

Time series model

The nature of our data (time series), as discussed by Woolridge (2008), is characterised by;

trends and seasonal patterns over time, and the dependency of observations across time.

Stationarity

In our paper, it is essential to understand if the dependent and independent variables are

stationary or not. Given that our dependent variable yt is binary, we do not need to conduct a

stationary test. Thus, we first proceed by testing the stationarity of our variables to prevent the

occurrence of spurious regressions, as discussed by Granger & Newbold (1973), which may


result in a high R2 even when the series are independent of each other. We use the Augmented

Dickey-Fuller test for unit root (see Dickey & Fuller, 1979) for models with a constant (M1),

with a time trend term included (M2), and a drift term included (M3):

∆𝑦𝑡 = 𝛼 + 𝛿𝑦𝑡−1 + 𝜖𝑡 (𝑀1)

∆𝑦𝑡 = 𝛼 + 𝛿𝑦𝑡−1 + 𝛽2𝑡 + 𝜖𝑡 (𝑀2)

∆𝑦𝑡 = 𝛼 + 𝛿𝑦𝑡−1 + 𝛽2∆𝑦𝑡−1 + 𝜖𝑡 (𝑀3)

Hypothesis:

H0: 𝛿 = 0 (The process is nonstationary)

H1: 𝛿 ≠ 0 (The process is stationary)

The resulting tau statistic:

𝐷𝐹𝜏 =𝛿

𝑠𝑒(𝛿)

is compared to the relevant critical values that were tabulated by David Dickey and Wayne

Fuller (ADF critical values) or a more extensive table by MacKinnon. If the tau statistic was

less than the critical value, we reject the null hypothesis (H0: 𝜹 = 0) and conclude that the

process is stationary.

The probit model

Estrella & Mishkin (1996) and Liu and Moench (2016), argue that the probit model is

appropriate in predicting business cycles because of its simplicity and ease of use.

Given that the dependent variable (recession indicator) is discrete:

𝑅𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛𝑡 = {1, 𝑖𝑓 𝑖𝑛 𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(1)

We estimate the probit model in the form of:

𝑃(𝑦 = 1|𝑥) = 𝐺 (𝛽0 + ∑(𝛽𝑖𝑋𝑖)

𝑛

𝑖=1

) = 𝐺(𝑧) (2)

where G is the standard normal cumulative density function (cdf):

𝐺(𝑧) = 𝜑(𝑧) ≡ ∫ 𝜑(𝑣)𝑧

−∞

𝑑𝑣 (3)

where 𝜑(v) is the standard normal probability density function (pdf).


The y variable is the binary recession indicator (rec) and the X’s are the credit spread

(credspr), market premium (marketprem) and their lags.

The advantage of the probit model, as discussed by Brooks (2014), is that equation (2) is

strictly between zero and one for all values of the parameters, circumventing the issues of the

linear probability model. Another advantage of the probit model is that it assumes that the error

terms follow the standard normally distribution. This results in error terms being

homoscedastic and not serially correlated.

Maximum Likelihood Estimator

The probit model is estimated using the maximum likelihood estimation (MLE) which – under

general conditions – are consistent, asymptotically normal, and asymptotically efficient (see

Wooldridge, 2008, Chapter 13).

Likelihood function:

𝑓(𝑦𝑖|𝑥𝑖; 𝛽) = [𝐺(𝑥𝑖𝛽)]𝑦𝑖[1 − 𝐺(𝑥𝑖𝛽)]1−𝑦𝑖 (4)

Where, y = 0, 1

Log-likelihood function:

log[𝑓(𝑦𝑖|𝑥𝑖; 𝛽)] = 𝑦𝑖𝑙𝑜𝑔[𝐺(𝑥𝑖𝛽)] + (1 − 𝑦1𝑖)𝑙𝑜𝑔[1 − 𝐺(𝑥𝑖𝛽)] (5)

MLE estimator:

�̂�𝑀𝐿𝐸 = arg min𝛽

∑{𝑦𝑖 log[𝐺(𝑥𝑖𝛽)] + (1 − 𝑦𝑖) log[1 − 𝐺(𝑥𝑖𝛽)]}

𝑛

𝑖=1

(6)

Partial Effect at the Average

partial effect of xj on 𝑝(𝑦 = 1|𝑋) is:

𝜕𝑝(𝑦 = 1|𝑋)

𝜕𝑥𝑗= 𝛽𝑗 ∙ 𝑔(𝑋𝛽) (7)

Where 𝑔(𝑧) ≡𝑑𝐺(𝑧)

𝑑𝑧 is the pdf of G(z), the cdf.

Hence, since 𝑔(𝑧) > 0 for all 𝑧 ∈ 𝑅, the sign is determined by 𝛽𝑗


Relative partial effect

The relative partial effect of 𝑥𝑗 and 𝑥𝑘 on 𝑝(𝑦 = 1|𝑋) is:

𝛽𝑗 ∙ 𝑔(𝑋𝛽)

𝛽𝑘 ∙ 𝑔(𝑋𝛽)=

𝛽𝑗

𝛽𝑘

(7)

Pseudo-R2

Lastly, we measure the goodness of fit using the pseudo-R2

𝑃𝑠𝑒𝑢𝑑𝑜 − 𝑅2 = 1 −1

1 +2(𝑙1 − 𝑙0)

𝑁

(8)

However, the pseudo-R2 has no natural interpretation and it is more informative to do a

Likelihood-Ratio (LR) test.

Likelihood-Ratio test

Hypothesis

H0: 𝜃 = 𝜃0

H1: 𝜃 = 𝜃1

LR test statistic:

𝐿𝑅 = 2(𝑙1 − 𝑙0) ~ 𝑋𝑞2 (9)

Where,

l1 is the log-likelihood value for the unrestricted model

l0 is the log-likelihood value for the restricted model

Data description

Our paper is based on data from the Federal Reserve Economic Data – St. Louis Fed (FRED)

and the National Bureau of Economic Research (NBER) from period 1993:12 to 2014:08.

We calculate credit spread by subtracting the Baa Moody’s with the Aaa Moody’s and the

excess return on the market portfolio by subtracting the value weighted market portfolio by the

risk-free rate. We measure business cycles fluctuations in the U.S. by using the binary

recession indicator which takes a value of 1 represents a recessionary period, while a value

of 0 represents an expansionary period. Recessions are defined by the National Bureau of

Economic Research (NBER) from the first day of the period following a peak and ends on the

day of the period of the trough.


An important consideration is that we use the first order difference of the credit spread because

of stationarity considerations. We also consider lagged terms for the market premium, the

logic being that recent historic market premiums may have an explanatory effect in the

probability of a recession.

Empirical results

Test for stationarity

The following table shows the results of the dickey-fuller and augmented dickey-fuller test for

the respective specifications.

Table 1: Dickey-Fuller and Augmented Dickey-Fuller test results

Variable Model Test

Statistic

1% Critical

value

5% Critical

value

Mackinnon

approx. p-value

Credit

Spread

(credspr)

M1 -2.039 -3.461 -2.880 0.2698

M2 -1.996 -3.991 -3.430 0.6035

M3 -2.039 -2.342 -1.651 0.0213**

Market

Premium

(marketprem)

M1 -14.113 -3.461 -.2880 0.0000***

M2 -14.085 -3.991 -3.430 0.0000***

M3 -14.113 -2.342 -1.651 0.0000***

* - 10%, ** - 5%, *** - 1% significance

From the table, we can reject the null hypothesis (H0: 𝜹 = 0) that credit spread is non-stationary

since the augmented dickey-fuller test (M3) is significant at the 5% level and the market

premium is stationary at the 1% significance level. As such, we can now use the variables as

per normal.

Specifying the model

The table 2 presents our empirical findings where we run a preliminary probit model (P1)

regressing the recession indicator (rec) on the credit spread (credspr) and market premium

(marketprem). We find that the coefficient of marketpremt is not significant at the 10% level.

Next, we hypothesise that the lag variables of credit spread and market premiums will have

explanatory power on the model since this data is available to the market at time t (P2). We

find that all coefficients are insignificant at the 5% level.


We then estimate a new model (P3) just on the lagged variables (credsprt-1, marketpremt-1)

and obtain significant coefficients at the 5% level.

Following that, we estimate the model (P4) on further lagged variables (credsprt-1, credsprt-2,

marketpremt-1, marketpremt-2). We find that the credsprt-2 is not significant at the 10% level.

Hence, we remove the credsprt-2 and re-run the regression (P5) which yields coefficients

significant at the 5% level.

Lastly, we add the marketpremt-3 variable in our final model (P6) and find that all coefficients

are now significant at the 5% level. We decide to stop here to avoid overfitting the model by

including some variables and not others.

From table 2, we can observe that the R2 increases as we add more variables into the model,

which is what we would expect due to the nature of the R2. However, we note that our final

model (P6) has an increase of 0.03 as compared to that of the previous model (P5). This would

suggest that there is indeed additional explanatory power by adding the variable (marketpremt-

3) into the model.


Table 2: Estimates of the models

* - 10%, ** - 5%, *** - 1% significance p-values in parenthesis

Model Constant credsprt credsprt-1 credsprt-2 marketpremt marketpremt-1 marketpremt-2 marketpremt-3 LR

statistic

Pseudo

R2

P1 -3.42***

(0.000)

1.99***

(0.000)

-0.04

(0.106)

59.88

(0.000)

0.359

P2 -3.41***

(0.000)

0.87

(0.521)

1.11

(0.390)

-0.05

(0.101)

-0.06*

(0.059)

63.35

(0.000)

0.380

P3 -3.31***

(0.000)

1.88***

(0.000)

-0.07**

(0.011)

59.28

(0.000)

0.356

P4 -3.44***

(0.000)

2.53*

(0.067)

-0.56

(0.661)

-0.06**

(0.027)

-0.07**

(0.019)

67.13

(0.000)

0.403

P5 -3.42***

(0.000)

1.95***

(0.000)

-0.07**

(0.020)

-0.08***

(0.006)

66.94

(0.000)

0.402

P6 -3.46***

(0.000)

1.98***

(0.000)

-0.07**

(0.011)

-0.07**

(0.015)

-0.07**

(0.020)

72.31

(0.000)

0.435


Interpretation of results

Using model P6, we estimate the partial effects of the independent variables:

Table 3: Partial effects at the average (PEA)

Variables credsprt-1 marketpremt-1 marketpremt-2 marketpremt-3

Estimates 0.1938***

(0.000)

-0.0072**

(0.016)

-0.0069**

(0.026)

-0.0069**

(0.026)

* - 10%, ** - 5%, *** - 1% significance p-values in parenthesis

Hence, a one unit increase in the lagged credit spread (credsprt-1) results in an increase of

19.38% in the probability of a recession; this is in line with economic theory since recessions

usually follow a period of tight credit (see Eckstein & Sinai, 1986).

In addition, a one unit increase in the lagged market premiums (marketpremt-1), (marketpremt-

2), (marketpremt-3), result in a decrease of -0.0072%, -0.0069%, -0.0069% in the probability of

a recession respectively. This is also in line with economic theory since a decrease in market

premiums may signal the beginning of a recession.

Next, we interpret the relative marginal effect of each variable:

Table 4: Relative marginal effect

credsprt-1 marketpremt-1 marketpremt-2 marketpremt-3

credsprt-1 1 -26.996 -28.142 -27.936

marketpremt-1 -0.037 1 1.042 1.035

marketpremt-2 -0.036 0.959 1 0.993

marketpremt-3 -0.036 0.966 1.007 1

Values are interpreted as the left column over the top row

From table 4, we can see that the credit spread generally has a much higher effect –

approximately 27 to 28 times more – on a recession relative to the market premium. In

contrast, the market premium lags have an equal effect relative to themselves on the

probability of a recession. We conclude from the interpretation of the relative marginal effects,

the credit spread dominates the market premium in explaining the probability of a recession.


Caveats or limitations

In this paper, we avoid overfitting the model by including some variables while excluding others

(the lagged variables of market premium and credit spread) to maximise the R2. Thus, we only

used models that have plausible economic justifications.

The salient limitations of our paper are contained in our data set. Firstly, we defined the credit

spread by using the difference between the Baa Moody’s and the Aaa Moody’s. This limits the

credit spread to changes in the investment grade bonds but not the junk bonds, which is greatly

distortive. Secondly, the length of the time taken into consideration is not sufficient because it

only includes two recessions.

The nature of the recession also plays a significant role as to whether the credit spread is a

significant variable or not. In the 2001 recession, which was the result of the dot-com bubble,

credit spreads were not affected since technology companies usually did not issue debt

instruments. Hence, we expect that the credit spread variable would not be significant during

this period. In contrast, given that the 2007-09 recession was largely caused by the credit

crisis, we expect the credit spread variable to be more significant during this period.

Lastly, we recognise that the model is extremely restricted since we only examine two financial

variables. Hence, it is necessary to complement the model by adding in more financial

variables as suggested by Estrella & Mishkin (1998).

Conclusion

In summary, we have examined the predictive effect of the credit spread and market premium

variables on the probability of falling into a recession. Consistently with economic theories,

credit spreads are indeed positively related to the probability of a recession while the market

premium is negatively related to the probability of a recession.

Our findings show that a contemporaneous regression was found to be insignificant. This is in

line with what we would expect as the data for the current period is unobservable, thus we

should only use a predictive regression where we use the lags of the variables. Yet, based on

our results, we find that the credit spread variable lagged by 2 periods is not significant. On

the other hand, lagged variables of market premium are found to be significant even in longer

lags. This suggest that market premium has a longer lasting effect on the probability of a

recession.


Appendix

Dickey-fuller test

Table 1a: testing stationarity of credit spread

MacKinnon approximate p-value for Z(t) = 0.2698

Z(t) -2.039 -3.461 -2.880 -2.570

Statistic Value Value Value

Test 1% Critical 5% Critical 10% Critical

Interpolated Dickey-Fuller

Dickey-Fuller test for unit root Number of obs = 248

. dfuller credspr


Z(t) -1.996 -3.991 -3.430 -3.130





. dfuller credspr, trend

p-value for Z(t) = 0.0213

Z(t) -2.039 -2.342 -1.651 -1.285



Z(t) has t-distribution


. dfuller credspr, drift


Table 1b: testing stationarity of market premium


Z(t) -14.113 -3.461 -2.880 -2.570





. dfuller marketprem

p-value for Z(t) = 0.0000

Z(t) -14.113 -2.342 -1.651 -1.285



Z(t) has t-distribution


. dfuller marketprem, drift


Z(t) -14.085 -3.991 -3.430 -3.130





. dfuller marketprem, trend


Graph 1: stationarity of credit spread and market premium

credit spread across time

market premium across time

01

23

4

cre

dspr

1995m1 2000m1 2005m1 2010m1 2015m1mydate

-20

-10

010

mark

etp

rem

1995m1 2000m1 2005m1 2010m1 2015m1mydate


Results of models

Table 2a: model 1

Table 2b: model 2

_cons -3.406281 .449589 -7.58 0.000 -4.287459 -2.525103

lagmarketprem1 -.0595957 .0316076 -1.89 0.059 -.1215456 .0023541

marketprem -.0462757 .0282069 -1.64 0.101 -.1015603 .0090088

lagcredspr1 1.107529 1.288979 0.86 0.390 -1.418824 3.633881

credspr .8653908 1.347013 0.64 0.521 -1.774706 3.505488

rec Coef. Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -51.548622 Pseudo R2 = 0.3806

Prob > chi2 = 0.0000

LR chi2(4) = 63.35

Probit regression Number of obs = 248

Iteration 4: log likelihood = -51.548622





. probit rec credspr lagcredspr1 marketprem lagmarketprem1

_cons -3.417634 .4524781 -7.55 0.000 -4.304475 -2.530794

marketprem -.0449001 .0277448 -1.62 0.106 -.099279 .0094788

credspr 1.990612 .4047868 4.92 0.000 1.197244 2.783979



Prob > chi2 = 0.0000

LR chi2(2) = 59.88







. probit rec credspr marketprem


Table 2c: model 3

Table 2d: model 4

_cons -3.313898 .4310778 -7.69 0.000 -4.158794 -2.469001

lagmarketprem1 -.0718618 .0282072 -2.55 0.011 -.1271469 -.0165766

lagcredspr1 1.877251 .3785698 4.96 0.000 1.135268 2.619234



Prob > chi2 = 0.0000

LR chi2(2) = 59.28







. probit rec lagcredspr1 lagmarketprem1

_cons -3.441639 .4632451 -7.43 0.000 -4.349582 -2.533695

lagmarketprem2 -.0741883 .0316352 -2.35 0.019 -.1361923 -.0121844

lagmarketprem1 -.0635819 .0286747 -2.22 0.027 -.1197834 -.0073805

lagcredspr2 -.5612897 1.278738 -0.44 0.661 -3.06757 1.94499

lagcredspr1 2.534688 1.382387 1.83 0.067 -.1747405 5.244116



Prob > chi2 = 0.0000

LR chi2(4) = 67.13







. probit rec lagcredspr1 lagcredspr2 lagmarketprem1 lagmarketprem2


Table 2e: model 5

Table 2f: model 6

_cons -3.423696 .4581781 -7.47 0.000 -4.321708 -2.525683

lagmarketprem2 -.0798865 .0290438 -2.75 0.006 -.1368113 -.0229617

lagmarketprem1 -.0658203 .0282429 -2.33 0.020 -.1211753 -.0104653

lagcredspr1 1.954201 .3923022 4.98 0.000 1.185303 2.723099



Prob > chi2 = 0.0000

LR chi2(3) = 66.94







. probit rec lagcredspr1 lagmarketprem1 lagmarketprem2

_cons -3.464885 .4937504 -7.02 0.000 -4.432618 -2.497152

lagmarketprem3 -.0709951 .0305015 -2.33 0.020 -.130777 -.0112132

lagmarketprem2 -.0704739 .0289724 -2.43 0.015 -.1272588 -.0136889

lagmarketprem1 -.0734668 .0289952 -2.53 0.011 -.1302962 -.0166373

lagcredspr1 1.983309 .4241308 4.68 0.000 1.152028 2.81459



Prob > chi2 = 0.0000

LR chi2(4) = 72.31







. probit rec lagcredspr1 lagmarketprem1 lagmarketprem2 lagmarketprem3


Graph 2: fit of models

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.2

.4.6

.81

1995m1 2000m1 2005m1 2010m1 2015m1mydate

Recession Indicator Pr(rec)

0.2

.4.6

.81

1995m1 2000m1 2005m1 2010m1 2015m1mydate


0.2

.4.6

.81

1995m1 2000m1 2005m1 2010m1 2015m1mydate


0.2

.4.6

.81

1995m1 2000m1 2005m1 2010m1 2015m1mydate


0.2

.4.6

.81

1995m1 2000m1 2005m1 2010m1 2015m1mydate


0.2

.4.6

.81

1995m1 2000m1 2005m1 2010m1 2015m1mydate



Partial marginal effects

Table 3

lagmarketprem3 -.0069375 .0031176 -2.23 0.026 -.0130478 -.0008272

lagmarketprem2 -.0068866 .0030114 -2.29 0.022 -.0127888 -.0009843

lagmarketprem1 -.007179 .002984 -2.41 0.016 -.0130276 -.0013304

lagcredspr1 .1938048 .0549895 3.52 0.000 .0860274 .3015823

dy/dx Std. Err. z P>|z| [95% Conf. Interval]

Delta-method

lagmarketp~3 = .6246748 (mean)



at : lagcredspr1 = .9685366 (mean)

dy/dx w.r.t. : lagcredspr1 lagmarketprem1 lagmarketprem2 lagmarketprem3

Expression : Pr(rec), predict()

Model VCE : OIM

Conditional marginal effects Number of obs = 246

. margins, dydx(*) atmeans


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Predicting U.S. business cycles: an analysis based on credit spreads and market premium

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