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 + 𝜖 𝑡 (𝑀1)
∆𝑦𝑡 = 𝛼 + 𝛿𝑦𝑡−1 + 𝛽2 𝑡 + 𝜖 𝑡 (𝑀2)
∆𝑦𝑡 = 𝛼 + 𝛿𝑦𝑡−1 + 𝛽2∆𝑦𝑡−1 + 𝜖 𝑡 (𝑀3)
Hypothesis:
H0: 𝛿 = 0 (The process is nonstationary)
H1: 𝛿 ≠ 0 (The process is stationary)
The resulting tau statistic:
𝐷𝐹𝜏 =
𝛿̂
𝑠𝑒(𝛿̂)
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:
𝑅𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 𝑡 = {
1, 𝑖𝑓 𝑖𝑛 𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(1)
We estimate the probit model in the form of:
𝑃(𝑦 = 1|𝑥) = 𝐺 (𝛽0 + ∑(𝛽𝑖 𝑋𝑖)
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(𝑥𝑖 𝛽)] 𝑦𝑖[1 − 𝐺(𝑥𝑖 𝛽)]1−𝑦𝑖 (4)
Where, y = 0, 1
Log-likelihood function:
log[𝑓(𝑦𝑖|𝑥𝑖; 𝛽)] = 𝑦𝑖 𝑙𝑜𝑔[𝐺(𝑥𝑖 𝛽)] + (1 − 𝑦1𝑖)𝑙𝑜𝑔[1 − 𝐺(𝑥𝑖 𝛽)] (5)
MLE estimator:
𝛽̂ 𝑀𝐿𝐸 = arg min
𝛽
∑{𝑦𝑖 log[𝐺(𝑥𝑖 𝛽)] + (1 − 𝑦𝑖) log[1 − 𝐺(𝑥𝑖 𝛽)]}
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 𝑥 𝑘 on 𝑝(𝑦 = 1|𝑋) is:
𝛽𝑗 ∙ 𝑔(𝑋𝛽)
𝛽 𝑘 ∙ 𝑔(𝑋𝛽)
=
𝛽𝑗
𝛽 𝑘
(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) ~ 𝑋 𝑞
2 (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
01234
credspr
1995m1 2000m1 2005m1 2010m1 2015m1
mydate
-20-10
0
10
marketprem
1995m1 2000m1 2005m1 2010m1 2015m1
mydate

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
.2.4.6.8
1
1995m1 2000m1 2005m1 2010m1 2015m1
mydate
Recession Indicator Pr(rec)
0
.2.4.6.8
1
1995m1 2000m1 2005m1 2010m1 2015m1
mydate
0
.2.4.6.8
1
1995m1 2000m1 2005m1 2010m1 2015m1
mydate
0
.2.4.6.8
1
1995m1 2000m1 2005m1 2010m1 2015m1
mydate
0
.2.4.6.8
1
1995m1 2000m1 2005m1 2010m1 2015m1
mydate
0
.2.4.6.8
1
1995m1 2000m1 2005m1 2010m1 2015m1
mydate

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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