Our study is based on the Minsky model.

According to Minsky’s theory of financial instability, economic dynamics are substantially determined by how firms finance their capital investments. At the beginning of the upward stage of the business cycle, secured financing from own development funds tends to prevail. Then gradually, as sales grow, firms actively switch to external financing by borrowing from banks.

In this case, elements of speculative financing or even Ponzi-financing are widely used, when new borrowings are needed to pay off existing debt. The process of increasing the share of speculative borrowing in total business financing leads to higher asset prices and increased investment. This is exactly what we have seen recently in the U.S. economy

The consequence is an increase in employment and demand in the economy, as well as in business profits, which, in turn, convinces businessmen and bankers of the usefulness of speculative financing, which brings good earnings. Such reactions, in the form of positive feedbacks, lead to a self-fulfilling spiral of credit expansion and economic growth.

However, this process gradually generates unsustainable debts and at a certain point in time, called the Minsky moment, leads to the inability of firms to repay their debts. From this point, credit and investment begin to decline, eventually leading to economic recession.

As Minsky has shown, in the absence of controls, both credit expansion and contraction can continue until the onset of financial and economic crisis. Since financial markets are inherently unstable systems, the primary task of central banks (CBs) is first to ensure the financial stability of the lending system and only second to control price stability. Thus, the task of a central bank is to prevent either an excessive expansion of credit or an excessive contraction of credit. The second part of this task is much better handled by the Central Bank than the first.

Since leaders are interested in increasing economic growth, they always put pressure on the Central Bank, and the latter will seek to facilitate the expansion of lending. This is what the business community wants as well.

But this policy is gradually transforming into a destabilizing factor, leading to a critical moment of Minsky.

In fact, the U.S. is actively raising interest rates in 2022 to stabilize the economy, but to arrive at their key rate, rates would have to be raised by almost 5%.

First of all, to describe the dynamics of investment lending in the expansion phase, we will use the differential equation

where I(t) is current investment in the economy. Equation (1) describes the dynamics of a self-reinforcing process with positive feedback. The solution to equation (1) is

The envelope curve, like the trend curve Lt which passes through all Mi-k , is well approximated by the logistic curve

At the intersection of the investment motion curve and the envelope of curve L we get a point, which is the coming Minsky moment (Mi+1), We get the date of the approximate beginning of the recession in the USA.

Approximately at this time, the next financial crisis in the U.S. should have occurred and the credit squeeze phase should have begun. To describe the dynamics of investment (IS) squeeze, we previously obtained a special formula for the downward stage of the Great Kondratieff Cycle (GKC)

where Im is the maximum projected investment volume at the point of the coming Minsky moment; T with M index is the projected time of the coming Minsky moment; lambda 0 – constant parameter. The parameter lambda 0 in the approximating formula (4) can be found by a similar downward stage of the investment cycle.

Thus, we have two approximating formulas (3) and (4), which approximate the expansion phase (3) and the subsequent contraction phase (4) of investment crediting after the beginning of the steady growth phase, respectively. These formulas can be used for short-term forecasting of the movement of investment I(t) in the U.S. economy.

**Forecast calculation of the GDP growth rate.**

To calculate the predicted rate of economic growth, we use the production function

where Y(t) is the current volume of national income (GDP); K(t) is the capital stock; L(t) is the number of workers employed in the economy; A(t) is technological progress; α is the share of capital in GDP; δ is the parameter characterizing increasing returns on scale of production (δ > 0); γ is the normalizing factor.

This formula was verified for the U.S. economy by a series of values of the main factors (K, A, and L).

We need to modify this formula to get more accurate data.

Our modification will involve adding a weighting factor to the formula, which will reflect the adjustment of GDP growth rates based on temperature changes and the resulting increase in electricity consumption (EC) in the region.

**Is there a dependence of GDP on energy consumption**

The first thorny question is whether GDP growth is dependent on EE consumption. To examine the relationship between India’s primary consumption and GDP, we first need to establish whether these time series are stationary or not. This is done by performing a unit root test, where the test identifies non-stationary variables, which means the presence of a stochastic trend that leads them to drift. The presence of a unit root is tested using the Kwiatkowski-Fillips-Schmidt unit root test. To check whether the series y (t) has a unit root or not, the following model is taken:

After establishing the non-stationary nature of GDP and Total Primary Cons at the level of first differences and the stationary nature at the first difference, the existence of any long-term equilibrium relationship between these two time series variables is investigated.

To study this, the concept of joint integration is applied. Co-integration implies an equilibrium relationship, which is a prerequisite for testing the long-run (equilibrium) relationship between selected variables. The joint integration methodology is a two-step process proposed by Engle and Granger (1987).

Using his formulas and concept we obtain that

Once the long-run relationship between primary energy consumption has been established, the short-run relationship is examined by applying the Granger Test criterion. Granger causality shows that lagged values of a variable provide statistically significant information for predicting another variable.

**Correction of energy consumption and temperature anomalies**

To correct for energy consumption, we need to find temperature anomalies, taking them into account to adjust the indicator for seasonality.

The range of data used also includes a forecast of weather in the region for the near term.

To find the temperature anomalies of the historical period, we use the function

```
data = m. make_future_dataframe(periods=x), (7)
expectations = m. predict(data), (8)
The programming language used is Python
```

where x – number of days for which the forecast is needed, data – previous data + used forecast, expectations – dataframe with future temperature readings.

This function will allow us to plot a preliminary weather behavior based on historical data. We need a regressor in this problem.

As a regressor we use an estimate of the temperature anomaly (formula 9) and its square (formula 8) – since extreme cold and heat usually lead to increased consumption. To do this, we complete the necessary columns (col1 , col2 ) in our dataframe using the formulas:

where regioni is the temperature data in period i.

To use regressors, let’s include them in the Prohpnet library[1] . Let’s take the variable M as the basis for Prohpnet.

Then use function (7) and assign the variable forecast to (8) and obtain the corrected data. To finally edit the data and predict behavior, we need to construct a new column using the function

To correct GDP growth for EС consumption in the region, we add the indicator, where i is the date.

Thus we get the formula

*In this way we can roughly calculate the themes of economic growth as a function of electricity consumption, *current national income, fixed capital, the number of workers employed in the economy, technological progress, α is the share of capital in GDP, δ is the parameter characterizing the increasing returns to scale of production (δ > 0), γ is the normalizing factor.

*[1] Prophet is an additive model-based time series data forecasting procedure in which nonlinear trends correspond to annual, weekly, and daily seasonality, as well as holiday effects. It works best with time series that have strong seasonal effects and multiple seasons of historical data. Prophet is robust to missing data and trend shifts and usually handles outliers well.*