An Introduction to Predicting Recessions

1. Overview
2. Implementation
- 2.1. Data Preparation
- 2.2. Model
3. References

1. Overview

We'll use the methods in this paper (Estrella, Arturo and Trubin, Mary, 2006) to predict recession via the yield curve. The model uses a long minus short-term interest rate spread as the single input variable. The spread is calculated using Treasury yields and is the 10 year minus the 3 month. We'll pull Treasury yields via the FRED API. The API codes are:

10 year	GS10
3 month	TB3MS

import pandas as pd
from fredapi import Fred
from scipy import stats
import matplotlib.pyplot as plt

2. Implementation

2.1. Data Preparation

The code below gathers the data.

key = pd.read_table("~/fred_api_key_pythoninfinance.txt")
key = str(key.columns.values[0])
fred = Fred(api_key=key)
ten_yr = fred.get_series('GS10')
three_mo = fred.get_series('TB3MS')
data = pd.concat([ten_yr, three_mo], axis=1, join='inner')
data.columns = ['long', 'short']
data

            long  short
1953-04-01  2.83   2.19
1953-05-01  3.05   2.16
1953-06-01  3.11   2.11
1953-07-01  2.93   2.04
1953-08-01  2.95   2.04
...          ...    ...
2023-01-01  3.53   4.54
2023-02-01  3.75   4.65
2023-03-01  3.66   4.69
2023-04-01  3.46   4.92
2023-05-01  3.57   5.14

[842 rows x 2 columns]

data.to_csv("treasury_data.csv")

data = pd.read_csv("treasury_data.csv", index_col=0)

2.2. Model

The predictive model is in a simple probit form:

\[P(R_{t+12}) = F(\alpha + \beta S_t)\]

where:

\(F\) denotes the cumulative normal distribution function.
\(S_t\) is the spread between short and long term interest rates at time t.
\(\alpha\) and \(\beta\) are estimated parameters.

(Estrella, Arturo and Trubin, Mary, 2006) estimated \(\alpha\) and \(\beta\) to be -0.6045 and -0.7374 respectively.

rec_prob = stats.norm.cdf(-0.6045 - 0.7374 * (data["long"] - data["short"]))
rec_prob = pd.DataFrame(rec_prob)
rec_prob = rec_prob.set_index(data.index)
rec_prob.columns = ["Recession Probability"]
rec_prob.plot.line()
plt.savefig('recession_probability.png', format='png')

None

3. References

Estrella, Arturo and Trubin, Mary (2006). The yield curve as a leading indicator: Some practical issues, Current issues in Economics and Finance.