Economics& Statistics lovers

✓✓ What is Consumer Surplus?

Consumer surplus, also known as buyer’s surplus, is the economic measure of a customer’s excess benefit. It is calculated by analyzing the difference between the consumer’s willingness to pay for a product and the actual price they pay, also known as the equilibrium price. A surplus occurs when the consumer’s willingness to pay for a product is greater than its market price.

Consumer surplus is based on the economic theory of marginal utility, which is the additional satisfaction a person derives by consuming one more unit of a product or service. The satisfaction varies by consumer, due to differences in personal preferences. According to the theory, the more of a product a consumer buys, the less willing he/she is to pay more for each additional unit due to the diminishing marginal utility derived from the product.

✓✓ Consumer Surplus and the Price Elasticity of Demand

Consumer surplus for a product is zero when the demand for the product is perfectly elastic. This is because consumers are willing to match the price of the product. When demand is perfectly inelastic, consumer surplus is infinite because a change in the price of the product does not affect its demand. This includes products that are basic necessities such as milk, water, etc.

Demand curves are usually downward sloping because the demand for a product is usually affected by its price. With inelastic demand, consumer surplus is high because the demand is not affected by a change in the price, and consumers are willing to pay more for a product.

In such an instance, sellers will increase their prices to convert the consumer surplus to a producer surplus. Alternatively, with elastic demand, a small change in price will result in a large change in demand. It will result in a low consumer surplus as customers are no longer willing to buy as much of the product or service with a change in price.

✓✓ Assumptions of the Consumer Surplus Theory

1. Utility is a measurable entity

The consumer surplus theory suggests that the value of utility can be measured. Under Marshallian economics, utility can be expressed as a number. For example, the utility derived from an apple is 15 units.

2. No substitutes available

There are no available substitutes for any commodity under consideration.

3. Ceteris Paribus

It states that customers’ tastes, preferences, and income do not change.

4. Law of diminishing marginal utility

It states that the more a product or service is consumed, the lower the marginal utility is derived from consuming each extra unit.

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SIMPLE LINEAR REGRESSION

Regression analysis is commonly used for modeling the relationship between a single dependent variable Y and one or more predictors. When we have one predictor, we call this "simple" linear regression:

E[Y] = β0 + β1X

That is, the expected value of Y is a straight-line function of X. The betas are selected by choosing the line that minimizes the squared distance between each Y value and the line of best fit. The betas are chosen such that they minimize this expression:

∑i (yi – (β0 + β1X))2

When we have more than one predictor, we call it Multiple Linear Regression:

Y = β0 + β1X1+ β2X2+ β2X3+… + βkXk

The fitted values (i.e., the predicted values) are defined as those values of Y that are generated if we plug our X values into our fitted model.
The residuals are the fitted values minus the actual observed values of Y.

There are assumptions associated with a linear regression model. They are:

ASSUMPTION 1
Linearity: The relationship between X and the mean of Y is linear.
THE REGRESSION MODEL IS LINEAR IN PARAMETERS
An example of model equation that is linear in parameters

Y = a + (β1*X1) + (β2*X2²)

Though, the X2 is raised to power 2, the equation is still linear in beta parameters. So the assumption is satisfied in this case.

ASSUMPTION 2
THE MEAN OF RESIDUALS IS ZERO

ASSUMPTION 3
Homoscedasticity: The variance of residual is the same for any value of X.
HOMOSCEDASTICITY OF RESIDUALS OR EQUAL VARIANCE
ASSUMPTION 4

NO AUTOCORRELATION OF RESIDUALS
This is applicable especially for time series data. Autocorrelation is the correlation of a time Series with lags of itself. When the residuals are auto correlated, it means that the current value is dependent of the previous (historic) values and that there is a definite unexplained pattern in the Y variable that shows up in the disturbances.

ASSUMPTION 5
THE X VARIABLES AND RESIDUALS ARE UNCORRELATED

ASSUMPTION 6
THE NUMBER OF OBSERVATIONS MUST BE GREATER THAN NUMBER OF XS
This can be directly observed by looking at the data.

ASSUMPTION 7
THE VARIABILITY IN X VALUES IS POSITIVE

ASSUMPTION 8
THE REGRESSION MODEL IS CORRECTLY SPECIFIED
This means that if the Y and X variable has an inverse relationship, the model equation should be specified appropriately:
Y=β1+β2∗ (1/X)

ASSUMPTION 9
NO PERFECT MULTICOLLINEARITY
There is no perfect linear relationship between explanatory variables.

ASSUMPTION 10
Normality: For any fixed value of X, Y is normally distributed.

NORMALITY OF RESIDUALS
The residuals should be normally distributed. If the maximum likelihood method (not OLS) is used to compute the estimates, this also implies the Y and the Xs are also normally distributed.
The method of ordinary least square (OLS) square (OLS)
Ø OLS estimators are expressed solely in terms of observable quantities. They are point estimators.
Ø The sample regression line passes through sample means of X and Y
Ø The mean value of the estimated Y^ is equal to the mean value of the actual Y: E(Y) = E(Y^)
Ø The mean value of the residuals U^i is zero: E (u^i) =0
Ø u^i are uncorrelated with the predicted Y^i and with Xi: That are ∑u^iY^i = 0; ∑u^iXi = 0
The assumptions underlying the method of least squares the method of least squares
Ø Ass 1: Linear regression model (in parameters)
Ø Ass 2: X values are fixed in repeated sampling
Ø Ass 3: Zero mean value of ui: E(ui|Xi) =0
Ø Ass 4: Homoscedasticity or equal variance of ui: Var (ui|Xi) = 2 [VS. Heteroscedasticity]
Ø Ass 5: No autocorrelation between the disturbances: Cov(ui,uj|Xi,Xj ) = 0 with i # j [VS. Correlation, + or - ]
Ø Ass 6: Zero covariance between ui and Xi Cov(ui, Xi) = E(ui, Xi) = 0
Ø Ass 7: The number of observations n must be greater than the number of parameters to be estimated
Ø Ass 8: Variability in X values. They must not all be the same
Ø Ass 9: The regression model is correctly specified
Ø Ass 10: There is no perfect multicollinearity between Xs
Precision or standard errors of least-squares estimates least-squares estimates
Ø In statistics the precision of an estimate is measured by its standard error (SE)

Ø var(β^2) = σ2 / βx2i
Ø se(β^2) = √ Var(β^2)
Ø var(β^1) = σ2 ∑X2i / n βx2i
Ø se(β^1) = √ Var(β^1)
Ø σ^ 2 = ∑u^2i / (n - 2)
Ø σ^ = √ σ^ 2 is standard error of the estimate
Precision or standard errors of least-squares estimates least-squares estimates
Features of the variance:
+ var (β ^2) is proportional to σ2 and inversely proportional to ∑ x2i
+ var (β ^1) is proportional to σ2 and ∑ X2i but inversely proportional to ∑ x2i and the sample size n.
+ cov (β^1, β ^2) = - var (β ^2) shows the independence between β ^1 and β ^2
Properties of least-squares estimator: The Gauss-Markov Theorem
Ø An OLS estimator is said to be BLUE if:
+ It is linear, that is, a linear function of a random variable, such as the dependent variable Y in the regression model
+ It is unbiased, that is, its average or expected value, E(β^2), is equal to the true value β2
+ It has minimum variance in the class of all such linear unbiased estimators
An unbiased estimator with the least variance is known as an efficient estimator
Gauss- Markov Theorem:
Given the assumptions of the classical linear regression model, the least-squares estimators, in class of unbiased linear estimators, have minimum variance, that is, they are BLUE

Keynes and classical economics
Excessive saving and interest rates

Investment is influenced by the level of income, by the expected course of future income, by anticipated consumption, and by the flow of savings. For example, a fall in savings will mean a cut in the funds available for investment, thus restricting investment.

The classical economists argued that interest rates would fall due to the excess supply of "loanable funds". This was the original Keynesian position, too, in which he followed both Malthus and John A. Hobson. The first diagram (See the first picture), adapted from the only graph in The General Theory, shows this process. Assume that fixed investment in capital goods falls from "old I" to "new I" (step a). Second (step b), the resulting excess of saving causes interest-rate cuts, abolishing the excess supply: so again we have saving (S) equal to investment. The interest-rate fall prevents the drop in production and employment.

Later on, however, excessive savings became Keynes' preoccupation; he believed that excessive saving had been Britain's and the United States' principal problem in the late 1920s, encouraging recession or even depression, so that only a demand-side kick could re-stimulate the economy.

The second diagram (See the second picture) summarizes his argument, assuming again that fixed investment falls (step A). First, saving does not fall much as interest rates fall, since the income and substitution effects of falling rates go in conflicting directions. Second, since planned fixed investment in plant and equipment is mostly based on long-term expectations of future profitability, that spending does not rise much as interest rates fall. So S and I are drawn as steep (inelastic) in the graph. Given the inelasticity of both demand and supply, a large interest-rate fall is needed to close the saving/investment gap. As drawn, this requires a negative interest rate at equilibrium (where the new I line would intersect the old S line).

EMERGENCE OF MACROECONOMICS
-----------------------------------------
Macroeconomics, as a separate branch of economics, emerged after the British economist John Maynard Keynes published his celebrated book The General Theory of Employment, Interest, and Money in 1936. The dominant thinking in economics before Keynes was that all the labors who are ready to work will find employment and all the factories will be working at their full capacity. This school of thought is known as the classical tradition.

However, the Great Depression of 1929 and the subsequent years saw the output and employment levels in the countries of Europe and North America fall by huge amounts. It affected other countries of the world as well. Demand for goods in the market was low, many factories were lying idle, and workers were thrown out of jobs. In the USA, from 1929 to 1933, the unemployment rate rose from 3 percent to 25 percent. Over the same period, aggregate output in the USA fell by about 33 percent. These events made economists think about the functioning of the economy in a new way.

The fact that the economy may have long-lasting unemployment had to be theorized about and explained. Keynes’ book was an attempt in this direction. Unlike his predecessors, his approach was to examine the working of the economy in its entirety and examine the interdependence of the different sectors and the subject of macroeconomics was born.

✓✓ Definition of Type I Error

In statistics, type I error is defined as an error that occurs when the sample results cause the rejection of the null hypothesis, in spite of the fact that it is true. In simple terms, the error of agreeing to the alternative hypothesis, when the results can be ascribed to chance.

Also known as the alpha error, it leads the researcher to infer that there is a variation between two observances when they are identical. The likelihood of type I error, is equal to the level of significance, that the researcher sets for his test. Here the level of significance refers to the chances of making type I error.

E.g. Suppose on the basis of data, the research team of a firm concluded that more than 50% of the total customers like the new service started by the company, which is, in fact, less than 50%.

✓✓ Definition of Type II Error

When on the basis of data, the null hypothesis is accepted, when it is actually false, then this kind of error is known as Type II Error. It arises when the researcher fails to deny the false null hypothesis. It is denoted by Greek letter ‘beta (β)’ and often known as beta error.

Type II error is the failure of the researcher in agreeing to an alternative hypothesis, although it is true. It validates a proposition; that ought to be refused. The researcher concludes that the two observances are identical when in fact they are not.

The likelihood of making such error is analogous to the power of the test. Here, the power of test alludes to the probability of rejecting of the null hypothesis, which is false and needs to be rejected. As the sample size increases, the power of test also increases, that results in the reduction in risk of making type II error.

E.g. Suppose on the basis of sample results, the research team of an organisation claims that less than 50% of the total customers like the new service started by the company, which is, in fact, greater than 50%.

✓✓ Key Differences Between Type I and Type II Error

1. Type I error is an error that takes place when the outcome is a rejection of null hypothesis which is, in fact, true. Type II error occurs when the sample results in the acceptance of null hypothesis, which is actually false.

2. Type I error or otherwise known as false positives, in essence, the positive result is equivalent to the refusal of the null hypothesis. In contrast, Type II error is also known as false negatives, i.e. negative result, leads to the acceptance of the null hypothesis.

3. When the null hypothesis is true but mistakenly rejected, it is type I error. As against this, when the null hypothesis is false but erroneously accepted, it is type II error.

4. Type I error tends to assert something that is not really present, i.e. it is a false hit. On the contrary, type II error fails in identifying something, that is present, i.e. it is a miss.

5. The probability of committing type I error is the sample as the level of significance. Conversely, the likelihood of committing type II error is same as the power of the test.

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✓✓ economic development

economic development, the process whereby simple, low-income national economies are transformed into modern industrial economies. Although the term is sometimes used as a synonym for economic growth, generally it is employed to describe a change in a country’s economy involving qualitative as well as quantitative improvements. The theory of economic development—how primitive and poor economies can evolve into sophisticated and relatively prosperous ones—is of critical importance to underdeveloped countries, and it is usually in this context that the issues of economic development are discussed.

Economic development first became a major concern after World War II. As the era of European colonialism ended, many former colonies and other countries with low living standards came to be termed underdeveloped countries, to contrast their economies with those of the developed countries, which were understood to be Canada, the United States, those of western Europe, most eastern European countries, the then Soviet Union, Japan, South Africa, Australia, and New Zealand. As living standards in most poor countries began to rise in subsequent decades, they were renamed the developing countries.

✓ There is no universally accepted definition of what a developing country is; neither is there one of what constitutes the process of economic development. Developing countries are usually categorized by a per capita income criterion, and economic development is usually thought to occur as per capita incomes rise. A country’s per capita income (which is almost synonymous with per capita output) is the best available measure of the value of the goods and services available, per person, to the society per year. Although there are a number of problems of measurement of both the level of per capita income and its rate of growth, these two indicators are the best available to provide estimates of the level of economic well-being within a country and of its economic growth.

✓ It is well to consider some of the statistical and conceptual difficulties of using the conventional criterion of underdevelopment before analyzing the causes of underdevelopment. The statistical difficulties are well known. To begin with, there are the awkward borderline cases. Even if analysis is confined to the underdeveloped and developing countries in Asia, Africa, and Latin America, there are rich oil countries that have per capita incomes well above the rest but that are otherwise underdeveloped in their general economic characteristics. Second, there are a number of technical difficulties that make the per capita incomes of many underdeveloped countries (expressed in terms of an international currency, such as the U.S. dollar) a very crude measure of their per capita real income. These difficulties include the defectiveness of the basic national income and population statistics, the inappropriateness of the official exchange rates at which the national incomes in terms of the respective domestic currencies are converted into the common denominator of the U.S. dollar, and the problems of estimating the value of the noncash components of real incomes in the underdeveloped countries. Finally, there are conceptual problems in interpreting the meaning of the international differences in the per capita income levels.

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In an attempt to calm the economy, control inflation, and support the beleaguered rupee, the State Bank of Pakistan’s Monetary Policy Committee (MPC) decided to raise the policy rate by 125 basis points.

Read more: https://thecurrent.pk/policy-rate-hiked-to-15-per-cent/

SBP raises policy rate to 14-year-high of 15 per cent - The Current SBP’s Monetary Policy Committee decided to raise the policy rate by 125 basis points (bps) to 15 per cent on Thursday.

✓✓ What Is R-Squared?

R-squared (R2) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. Whereas correlation explains the strength of the relationship between an independent and dependent variable, R-squared explains to what extent the variance of one variable explains the variance of the second variable. So, if the R2 of a model is 0.50, then approximately half of the observed variation can be explained by the model's inputs.

✓✓ R-squared values range from 0 to 1 and are commonly stated as percentages from 0% to 100%. An R-squared of 100% means that all movements of a security (or another dependent variable) are completely explained by movements in the index (or the independent variable(s) you are interested in).

In investing, a high R-squared, between 85% and 100%, indicates the stock or fund's performance moves relatively in line with the index. A fund with a low R-squared, at 70% or less, indicates the security does not generally follow the movements of the index. A higher R-squared value will indicate a more useful beta figure. For example, if a stock or fund has an R-squared value of close to 100%, but has a beta below 1, it is most likely offering higher risk-adjusted returns.

✓✓ R-Squared vs. Adjusted R-Squared

R-Squared only works as intended in a simple linear regression model with one explanatory variable. With a multiple regression made up of several independent variables, the R-Squared must be adjusted.

The adjusted R-squared compares the descriptive power of regression models that include diverse numbers of predictors. Every predictor added to a model increases R-squared and never decreases it. Thus, a model with more terms may seem to have a better fit just for the fact that it has more terms, while the adjusted R-squared compensates for the addition of variables and only increases if the new term enhances the model above what would be obtained by probability and decreases when a predictor enhances the model less than what is predicted by chance.

In an overfitting condition, an incorrectly high value of R-squared is obtained, even when the model actually has a decreased ability to predict. This is not the case with the adjusted R-squared.

✓✓ Limitations of R-Squared

R-squared will give you an estimate of the relationship between movements of a dependent variable based on an independent variable's movements. It doesn't tell you whether your chosen model is good or bad, nor will it tell you whether the data and predictions are biased. A high or low R-square isn't necessarily good or bad, as it doesn't convey the reliability of the model, nor whether you've chosen the right regression. You can get a low R-squared for a good model, or a high R-square for a poorly fitted model, and vice versa.

✓✓ What Is a Good R-Squared Value?

What qualifies as a “good” R-Squared value will depend on the context. In some fields, such as the social sciences, even a relatively low R-Squared such as 0.5 could be considered relatively strong. In other fields, the standards for a good R-Squared reading can be much higher, such as 0.9 or above. In finance, an R-Squared above 0.7 would generally be seen as showing a high level of correlation, whereas a measure below 0.4 would show a low correlation. This is not a hard rule, however, and will depend on the specific analysis.

Autonomous consumption

Definition of autonomous consumption: This is the level of consumption which does not depend on income. The argument is that even with zero income you still need to buy enough food to eat – either through borrowing or running down savings.

Autonomous consumption in the Keynesian model

In the Keynesian model of aggregate expenditure, autonomous consumption plays an important role.
C = a +bY. In this formula a is the level of autonomous consumption, where b is the marginal propensity to consume out of income.

What determines autonomous consumption?

The level of autonomous consumption depends upon:

•Assets such as houses – with assets, people can gain equity withdrawal – remortgaging the house to take out a loan.

•Expectations of future income. Expected future income gives consumers more confidence to borrow.

•Difficulty/ease of borrowing money to finance the autonomous consumption. Payday loans are often used by people in low-income who want to maintain day to day expenditure.

•Time period. In the short-term, people have commitments to pay bills so autonomous consumption is quite high. However, if the period of no income persists, individuals will ‘downsize’ – ending phone contracts, move to cheaper accommodation, and every trying to grow your own vegetables.

•Levels of saving

•Minimum standards of living and ideas of absolute poverty.


This is consumption that is influenced by levels of income. With rising income, people can spend more. In the equation below, induced consumption is given by formula b(Y) where b equals the marginal propensity to consume

Example
To understand better, let us take autonomous consumption example:

Lisa had a job with a fair salary. She lived in a small apartment for rent. She paid for all her necessities like food, rent, utilities, healthcare, and mortgage payments on time and non-essential goods and services utilizing her disposable income.
Unfortunately, she lost her job due to downsizing caused by a financial crisis
in her company. She tried to take another job but couldn’t find one immediately. So, she canceled all her vacation plans and stopped spending on other usual discretionary events like shopping sprees, eating-outs, and online subscriptions. By canceling non-essential goods and services, she prioritized spending on essentials that she could not avoid.
Due to a lack of cash inflow, she managed to pay for necessities by utilizing her savings and borrowings. After two months, she finally found a suitable job and slowly paved her way back to how she was living before

Understand Demand in Dept

To an economist, demand refers to “the quantity of a product that purchasers are willing and able to buy at various prices per period of time, all other things being equal”. Definitions are of critical importance in Economics, so let us break this definition down to understand in some depth what it means.

1. Quantity: This refers to the numerical quantity of a product that is being demanded.

2. Product: This is a general term that simply refers to the item that is being traded. It can be used for goods or services. We could also stretch this to include tradable items like money or other financial assets such as shares.

3. Purchasers: Often referred to as ‘consumers’, although they may simply be intermediaries in the supply chain, e.g., Nestlé purchasing large amounts of cocoa to be used in the production of chocolate for sale to the final consumer. We can consider an individual’s demand for a product or, more usefully, we can aggregate this to look at the demand for the market as a whole.

4. Willing to buy: Purchasers must want a product if they are going to enter into the market with the intention of buying it.

5. Able to buy: To an economist, the notional demand for a product, which emerges from wanting it, must be backed by purchasing power if the demand is to become an effective demand. Sellers are only willing to sell a product if the purchaser has the money to pay for the product. It is this effective demand that is of particular importance for economists.

6. Various prices: Prices are crucial to the functioning of a market. Although many things influence demand for a product, it is at the time of purchase, when we have to hand over our money and pay the price that we really judge whether the product is value for money – in other words, whether we really are willing and able to buy it. As the price goes up, and provided no other changes have occurred, more and more people will judge the product to be less worthwhile.

7. Per period of time: Demand must be time related. It is of no use to say that the local McDonald’s sold 20 Big Macs to consumers unless you specify the time period over which the sales occurred. If that was per minute then demand is high, but if that was per week then this would show there is little demand for Big Macs in this particular market.

8. Other things being equal: There are numerous potential influences on the demand for a product. Understanding the connections between the various influences is very difficult if many of these elements are changing simultaneously. This is why it is necessary to apply the ceteris paribus assumption.

✓✓ Catch-Up Effect

The catch-up effect is a theory that all economies will eventually converge in terms of per capita income, due to the observation that underdeveloped economies tend to grow more rapidly than wealthier economies. In other words, the less wealthy economies will literally "catch-up" to the more robust economies. The catch-up effect is also referred to as the theory of convergence.

✓✓ The catch-up effect, or theory of convergence, is predicated on a couple of key ideas.

One is the law of diminishing marginal returns—the idea that as a country invests and profits, the amount gained from the investment will eventually decline as the level of investment rises. Each time a country invests, they benefit slightly less from that investment. So, returns on capital investments in capital-rich countries are not as large as they would be in developing countries.

This is backed up by the empirical observation that more developed economies tend to grow at a slower, though more stable, rate than less developed countries. According to the World Bank, high-income countries averaged 1.6% gross domestic product (GDP) growth in 2019, versus 3.6% for middle-income countries and 4.0% GDP growth in low-income countries.

Underdeveloped countries may also be able to experience more rapid growth because they can replicate the production methods, technologies, and institutions of developed countries. This is also known as a second-mover advantage. Because developing markets have access to the technological know-how of the advanced nations, they often experienced rapid rates of growth.

✓✓ Limitations to the Catch-Up Effect

Although developing countries can see faster economic growth than more economically advanced countries, the limitations posed by a lack of capital can greatly reduce a developing country's ability to catch up. Historically, some developing countries have been very successful in managing resources and securing capital to efficiently increase economic productivity; however, this has not become the norm on a global scale.

-----Economist Moses Abramowitz wrote about the limitations to the catch-up effect. He said that in order for countries to benefit from the catch-up effect, they would need to develop and leverage what he called "social capabilities." These include the ability to absorb new technology, attract capital, and participate in global markets. This means that if technology is not freely traded, or is prohibitively expensive, then the catch-up effect won't occur.

-----Another major obstacle to the catch-up effect is that per capita income is not just a function of GDP, but also of a country's population growth. Less developed countries tend to have higher population growth than developed economies. According to the World Bank figures for 2019, more developed countries (OECD members) experienced 0.5% average population growth, while the UN-classified least developed countries had an average 2.3% population growth rate.

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