Two models for forecasting the effects of Interest rates and GDP with code for the models in Python.

For the first model that relates GDP and interest rates, I would use it as a guide for my macroeconomic outlook and to help me identify investment opportunities or risks. If I believed that interest rates were likely to rise in the near future, I would expect that to have a negative impact on GDP growth, and therefore, I might adjust my portfolio to reduce exposure to sectors that are particularly sensitive to interest rate changes, such as housing, construction, or consumer durables.

On the other hand, if I believed that interest rates were likely to fall, I might look for opportunities to increase exposure to interest rate-sensitive sectors or to invest in bonds or other fixed-income securities that could benefit from the lower rates.

For the second model that relates changes in interest rates to changes in GDP, I would use it to help me anticipate how the markets might react to changes in interest rates by the Federal Reserve or other central banks. If I believed that interest rates were likely to rise, I would expect to see a decrease in investment spending and GDP growth, which could lead to a sell-off in equities and other risk assets.

Conversely, if I believed that interest rates were likely to fall, I might anticipate an increase in investment spending and GDP growth, which could lead to a rally in risk assets. Based on these expectations, I would adjust my portfolio accordingly, potentially by increasing or decreasing exposure to equities, fixed-income securities, or other asset classes that are likely to be affected by changes in interest rates.

One possible model that could capture the relationship between interest rates and GDP is the following:

GDP = β0 + β1 * Interest Rate + ε

where:

- GDP represents the dependent variable, i.e. the level of gross domestic product in an economy

- Interest Rate represents the independent variable, i.e. the prevailing interest rate in the economy

- β0 is the intercept, representing the level of GDP when the interest rate is zero

- β1 is the slope coefficient, representing the change in GDP for each unit change in the interest rate

- ε is the error term, representing the random variation in GDP that is not explained by the interest rate

This model assumes a linear relationship between GDP and interest rates, where an increase in the interest rate leads to a decrease in GDP, and vice versa. However, it is important to note that this is a highly simplified model and there are many other factors that can affect GDP, such as fiscal policy, consumer sentiment, and external shocks.

Sure! One possible model that captures the relationship between changes in interest rates and changes in GDP is called the “IS” (Investment-Saving) curve in macroeconomics.

The IS curve represents the equilibrium relationship between the real interest rate and the level of output (i.e. real GDP) in an economy, assuming that prices are fixed in the short run. The model is based on the assumption that output (Y) is determined by the intersection of aggregate demand and aggregate supply. Aggregate demand is composed of consumption (C), investment (I), government spending (G), and net exports (NX). Aggregate supply is assumed to be fixed in the short run.

The IS curve can be written as follows:

Y = C(Y-T) + I(r) + G + NX(e)

where:

- Y is the level of output (real GDP)

- T is the level of taxes

- r is the real interest rate

- C(Y-T) represents consumption as a function of disposable income

- I(r) represents investment as a function of the real interest rate

- G is government spending

- NX(e) represents net exports as a function of the exchange rate (e)

The key assumption of the IS curve is that investment is negatively related to the real interest rate. In other words, when the interest rate is high, firms are less likely to borrow money to finance investment projects, and investment spending decreases. Conversely, when the interest rate is low, firms are more likely to borrow and invest, and investment spending increases.

If we take the derivative of the IS curve with respect to the real interest rate (r), we can see the effect of changes in the interest rate on output (Y):

dY/dr = -dI/dr

This equation tells us that when the interest rate increases (i.e. dI/dr is negative), investment spending decreases, which in turn reduces output (Y). Similarly, when the interest rate decreases (i.e. dI/dr is positive), investment spending increases, which leads to an increase in output (Y).

Therefore, the IS curve shows a negative relationship between the real interest rate and output (Y), reflecting the idea that changes in the interest rate can affect investment spending and, consequently, GDP.

Sure! Here’s an implementation of the first model in Python using the statsmodels package:

python

import pandas as pd

import numpy as np

import statsmodels.api as sm

# Load the data

data = pd.read_csv(‘data.csv’) # Replace with the filename of your data

interest_rates = data[‘Interest Rate’]

gdp = data[‘GDP’]

# Define the model

X = sm.add_constant(interest_rates) # Add a constant term to the independent variable

model = sm.OLS(gdp, X)

# Fit the model

results = model.fit()

# Print the summary of the regression results

print(results.summary())

In this code, we first load the data into two arrays, `interest_rates` and `gdp`. We then use the `add_constant` function from `statsmodels` to add a constant term to the independent variable, and create an instance of the `OLS` (ordinary least squares) class to define the regression model. We fit the model using the `fit` method, and print the summary of the regression results using the `summary` method of the results object.

The output will include information such as the coefficients of the regression equation, the standard errors of the coefficients, the R-squared value, and the p-values of the coefficients, among other things. This information can be used to evaluate the significance of the relationship between interest rates and GDP, and to make informed investment decisions based on the results.

Certainly! Here’s an implementation of the IS model in Python using the `scipy` package to solve for the equilibrium level of output:

python

import numpy as np

from scipy.optimize import fsolve

# Define the parameters of the model

T = 1000 # Taxes

C = 1000 # Autonomous consumption

G = 1000 # Government spending

NX = 0 # Net exports

e = 1 # Exchange rate

def investment(r):

??“”"Investment function”“”

??return 1000 - 50*r # Example function, replace with your own

def aggregate_demand(Y, r):

??“”"Aggregate demand function”“”

??return C*(Y-T) + investment(r) + G + NX*e

def is_curve(r):

??“”"IS curve equation”“”

??return aggregate_demand(Y, r) - Y

# Solve for the equilibrium level of output

r = 0.05 # Initial guess for the real interest rate

Y = fsolve(is_curve, 5000, args=(r,))

print(“Equilibrium output:“, Y[0])

In this code, we first define the parameters of the model, including taxes, autonomous consumption, government spending, net exports, and the exchange rate. We then define the investment function and the aggregate demand function, which represents the sum of consumption, investment, government spending, and net exports as a function of output (Y) and the real interest rate (r).

We also define the IS curve equation, which represents the difference between aggregate demand and output, and use the `fsolve` function from `scipy.optimize` to solve for the equilibrium level of output (Y) that satisfies the IS curve equation.

The output will be the equilibrium level of output, given the initial guess for the real interest rate. This information can be used to inform investment decisions, such as whether to increase or decrease exposure to sectors that are sensitive to changes in interest rates.

--h, Henry Carstens , Portfolio Manager and Head of Research, Aargo Trade