Assignment Code: MEC-002/2021-22

Course Code: MEC-002

Assignment Name: Macroeconomic Analysis

Year: 2021-2022

Verification Status: Verified by Professor

Note: Answer all the questions. While questions in Section A carry 20 marks each (to be answered in about 500 words each) those in Section B carry 12 marks each (to be answered in about 300 words each). In the case of numerical questions word limits do not apply.

Section A

1. What is meant by steady state in the Solow model? Explain how Golden Rule is different from steady state.

Ans) sy=i

Saving equals investment, as shown in the equation above, which is a prerequisite for economic equilibrium. Investment per unit of effective labour equals saving per unit of effective labour, as shown in the equation:

i = sy

Since y = f(k) we can write the equation as

i = sf(k)     …. (1.1)

The graph above depicts the link between current capital stock (k) and new capital accumulation I in terms of 'per effective labour'. Investment leads to an increase in capital stock. As a result, the difference in capital stock between two years is equal to the amount of investment made during the year. In other words, the rate of investment is equal to the rate of growing capital stock. We can express (1.1) as an effective labour term.

k = sf(k)

where k denotes the rate of growth in k. (In general we put a dot over a variable to represent its growth rate). I The above equilibrium condition holds true in an economy where capital stock does not depreciate, population does not grow, and technological advancement does not occur. Let us pretend that there is no population increase and no technological advancement in the economy for the time being.

Growth of Capital and Steady State

The Solow model assumes that existing capital depreciates at the rate δ. As a result, a total of K dollars of capital is depreciated each year. Investment and depreciation move in opposite directions, resulting in growth that is the net of the two.

k(t) = i(t) - δk(t) I

since i = sf(k(t))

k(t) = sf(k(t))- δk(t)

Technological Progress and Steady State

To explain growth in output per effective labour, we need to introduce technological progress in the Solow model. As stated earlier technological progress is assumed to be labour-augmenting. Thus technological progress increases the quantity of effective labour (AL). Let us assume that the rate of technological progress is g.

The change in k over time is now modified as:

k(t) = sf (k(t)) - (n + g + δ) k(t)

The above equation is the key equation of the Solow model of growth

The Golden Rule

Let us assume that saving rate rises while n, g, and S remain unchanged (see Fig. 3.7). Since i = sf(k) id be higher investment which in turn will lead to capital accumulation and output gm and the economy will eventually reach to a new steady state with higher capital output.

When saving rate rises from s1 to s2 the investment curve shifts up from s1f(k) to s2f(k).  Thus the economy reaches a new steady state k2 after going through the process of capital accumulation as described above.

It may lead us to think that a high rate of saving is always desirable since higher saving results in higher capital stock and output. You may think that if saving is 100% there will be largest possible output and capital stock in the economy. At various levels of s different steady state are achieved with different levels of capital accumulation. However, there is an optimum level of capital accumulation which is called the golden rule level of capital.

 At the golden rule level of capital the level of s is such that the consumption per effective labour is maximum at the steady state. Why is consumption per effective labour maximized? This is because individuals, who make up the economy, are not concerned about the capital stock or total output of the economy. For them what is important is the amount of output they consume. Among the various steady states one that maximizes consumption per effective labour is thus the most desirable one and hence called the 'golden rule level'.

Income which is equal to output is allocated on consumption and saving (which is equal to investment), that is, Y = C + 1. Steady state consumption is output net of investment. Thus

c* = y* - i*

We can write the above as

C* = f(k*) – (n + g + δ)k*

As increase in steady state capital has contrasting effect on steady state consumption - more capital leads to more output which contributes positively to consumption, but it also means higher break even investment (n+g+ δ)k

Steady state consumption is the gap between the steady state output and steady state break-even investment, which is maximised at k*gold level of capital per effective labour. Recall that the slope of the production function is the marginal product of capital MPK. c*gold level of consumption (golden rule level) the slope of production function equals the slope of break-even investment, that is,

MPK= (n+g+ δ)

Or

(MPK- δ)= (n + g)

At the golden rule level of capital, the MPK net of depreciation is equal to the rate of growth of total output (n + g). The golden rule steady state is not achieved automatically. It requires a particular rate of saving sgold

2. Explain how the permanent income hypothesis reconciles the difference between short-run and long-run consumption behaviour.

Ans) The permanent income hypothesis (PIH) is a model in the field of economics to explain the formation of consumption patterns. In its simplest form, the hypothesis states changes in permanent income (human capital, property, assets), rather than changes in temporary income (unexpected income), are what drive changes in consumption.

The formation of consumption patterns opposite to predictions was an outstanding problem faced by the Keynesian orthodoxy. Friedman's predictions of consumption smoothing, where people spread out transitory changes in income over time, departed from the traditional Keynesian emphasis on a higher marginal propensity to consume[β] out of current income.

Friedman's permanent income hypothesis provides an alternative explanation to the apparent discrepancy between cross-sectional and time series data on consumption. The permanent income hypothesis is also founded on the Fisherian theory of consumption as an intertemporal choice. However, unlike the life-cycle hypothesis, Friedman does not postulate that income follow a regular pattern over the life cycle of an individual; he instead argues that individuals experience random and temporary changes in their income from time to time. Accordingly, Friedman views the current income in any period ( Y, ) as consisting of two components: permanent income (Ytp) and transitory income (Y1t) Permanent income is that part of the income which we expect to prevail over the long run. Friedman interprets this as the long run average income of the individual, i,e

Transitory income is any random deviation from this average,

A positive transitory income implies that the current income exceeds the permanent income; a negative transitory income implies that the current income is less than the permanent income. Since

i.e., current consumption of the household depends only on the permanent income, my increase in the transitory part of the current income, which leaves the permanent income unchanged, will have no impact on the level of current consumption. Let us now see how Friedman's permanent income hypothesis solves the apparent puzzle in the consumption data. According to Friedman's hypothesis, the average propensity to consume (C, / Y,) depends on the ratio of permanent to current income Y," / Y,. Thus, when current income temporarily rises above the permanent income the average propensity to consume falls; the opposite happens when current income temporarily falls below the permanent income. Now when we are looking at cross- Decision-Ma king sectional data of different households at any point of time, typically the high-income group will contain some people with a high transitory income, who will have a lower propensity to consume than the average. Similarly, the low-income group will contain some people with a low transitory income, who will have a higher propensity to consume than the average. As a result, we will observe a falling average propensity to consume as we move from the lower to the higher income group. On the other hand, when we are considering long run time series data, the random fluctuations tend to even out so that any increase in income in the long run reflects a permanent increase in the average income level. Hence in the long run time series data we are likely to observe a constant average propensity to consume.

Section B

3. Policy makers should stick to rules instead of pursuing discretionary polices. Do you agree with the above statement? Substantiate your answer.

Ans) The credibility of a proclaimed policy regulation is based not just on past experience with a government's capacity to keep promises, but also on a logical assessment of a government's future ability to keep promises. In this light, governments, like private economic entities, have goals that they want to attain through policy actions. Assume we define a policy rule to be time-consistent or dynamically consistent if the policy chosen under the rule is optimal for the remaining part of the time-horizon at every instant over that time-horizon, taking as given the policies chosen before that instant and assuming that policy will be similarly optimally chosen at every future instant. If governments have the ability to change policy at any moment in the future, a policy rule that is published will not be credible unless it is time consistent. If a policy rule is not time-consistent, it will not be optimal for the government to follow the rule's policy at some point in the future. Deviating from the rule at that point in time will benefit the government.

The policy rule that is optimal over the full time horizon may not be time consistent, which could present a problem. Finn Kydland and Edward Prescott first suggested this concept in a 1977 research report. In a well-known example, Kydland and Prescott demonstrate their point by looking at flood-prevention policies. Assume that the socially desirable conclusion is not to develop dwellings in a flood-prone location, but rather to undertake certain costly flood-control measures, such as the construction of dams and one embankment, if settlements already exist there. Nobody would establish houses in a currently empty flood-prone location if the government declared that it would never undertake flood control measures there, and if private agents thought that the government would follow this policy guideline. The rational agent, on the other hand, will not believe this policy norm because he knows that after he and others develop structures in that area, the government will find it necessary to institute flood-control measures. As a result, society will be obliged to accept a sub-optimal outcome in which private agents construct buildings in flood-prone areas, with the government intervening to construct dams and embankments.

If we rule out the possibility of passing legislation prohibiting the construction of structures in flood-prone areas, the only way the government can make the policy rule (that it will never undertake any flood-control measures in a currently uninhabited flood-prone area) credible is to commit to its implementation over time. The government must be able to persuade the public that it will not be able to follow policies that will be optimal for it at future points in time. Thus, not only might policy rules provide more optimal outcomes over time than discretionary policy choices, but the ability to use discretion in policy making itself must be limited if optimal policy rules are to be credible.

One apparent approach for the government to commit to a policy rule is to introduce legislation that makes breaking the rule costly in the future. However, amending this legislation may be difficult and time consuming if unforeseeable events occur that necessitate deviating from the norm, or if it is discovered that key assumptions used in the rule's formulation are incorrect. Another option to make an ideal policy norm credible without losing the freedom to use discretion in emergencies is for the government to outsource responsibility for the policy to an autonomous agency with a different objective function than the public sees. As a result, governments frequently delegate monetary policy to an independent central bank, with the premise that a monetary policy regulation aimed at lowering inflation would be more believable if implemented by financiers who are known to be anti-inflation rather than politicians.

4. Explain in brief the salient features of real business cycle theory. In what respects is it different from other theories of business cycle?

Ans) Real business-cycle theory (RBC theory) is a class of new classical macroeconomics models in which business-cycle fluctuations are accounted for by real (in contrast to nominal) shocks. Unlike other leading theories of the business cycle,[citation needed] RBC theory sees business cycle fluctuations as the efficient response to exogenous changes in the real economic environment. That is, the level of national output necessarily maximizes expected utility, and governments should therefore concentrate on long-run structural policy changes and not intervene through discretionary fiscal or monetary policy designed to actively smooth out economic short-term fluctuations.

According to RBC theory, business cycles are therefore "real" in that they do not represent a failure of markets to clear but rather reflect the most efficient possible operation of the economy, given the structure of the economy.

If we were to take snapshots of an economy at different points in time, no two photos would look alike. This occurs for two reasons:

Many advanced economies exhibit sustained growth over time. That is, snapshots taken many years apart will most likely depict higher levels of economic activity in the later period.

There exist seemingly random fluctuations around this growth trend. Thus given two snapshots in time, predicting the latter with the earlier is nearly impossible.

A common way to observe such behavior is by looking at a time series of an economy's output, more specifically gross national product (GNP). This is just the value of the goods and services produced by a country's businesses and workers.

5. Explain why firms may offer a higher wage to workers than the equilibrium wage rate.

Ans) Efficiency wage theories are clearly non-Walrasian theories in as much as they postulate payment of wages that are higher than market-clearing wages. The persistence of unemployment follows as a direct consequence of higher wages. The efficiency wage theories rationalise the existence of higher than market clearing real wages.

Broadly speaking, firms pay higher than market-clearing real wages because the benefits accruing from higher wages are more than the cost of paying higher wages. The higher benefits can accrue for the following reasons:

1. At a very basic level, higher wages enable higher consumption for workers, including higher nutrition, and this is expected to increase the work capacity of the hired workers. The point is more valid at lower levels of standards of living than are prevalent in the developed economies.

2. Higher wages may get into the pool of workers with a higher reservation wage, i.e., the minimum wage that should be offered to a worker to induce him to supply his labour on the market. Workers with a higher reservation wage are expected to have superior abilities along directions that cannot be I directly observed and duly compensated for on the market. These higher abilities in the pool of employed workers are expected to benefit the firm.

3. A higher than market wage can build loyalty and a sense of belonging among workers and induce higher effort. This point is better understood in the context of the opposite situation of a lower wage, which is expected to have effects like generating anger and a desire for revenge, thereby leading 1 even to a sabotage by the workers.

4. At a more sophisticated level, a higher wage generates incentives for workers to avoid work-shirking behaviour in situations where the firms c cannot monitor the work effort perfectly. Workers do not want to be caught shirking in such valuable jobs, for they could be fired if caught shirking and may be able to replace the job, if at dl, by one which pays only a market clearing and hence a lower wage.

Some of the above ideas have been developed into more formal models in the literature. In the next Section you will go through one such model that analyses i the determination sf efficiency wages.

The efficiency wage models postulate and rationalise a higher than market clearing wage on the ground that the benefits accruing from higher wages are more than the costs of maintaining wages at a higher level. The benefits come from increased efficiency of workers. The increased efficiency could be due to increased physical efficiency of workers obtaining higher wages, or due to the engendering of a sense of loyalty and belonging among workers, or even due to avoidance of work shirking by workers who do not want to lose high paying jobs if caught shirking. The efficiency wage model not only rationalises the existence of persistent unemployment, but also produces a larger effect on employment in the short run. The shortcoming of an efficiency wage model using a simple version of the effort function is that it implies that there is no increasing trend in the real wage even in the long run. This is contrary to empirically observed facts. The shortcoming can be easily remedied by using a more complex effort function.

The contracting and insider-outsider models rationalise wage rigidity with reference to the fact that wages are determined long term contracts between workers and firms and are not necessarily set at the market-clearing level in each period. This immediately rationalises wage rigidity and unemployment. The insider-outsider models provide the insight that though it is in the interest of the unemployed workers (outsiders) that wages are contracted to be low so that employment is higher, the unemployed in a non-competitive economy have no power in the matter, as wages are determined through bargaining between the employed workers (insiders interested in higher wages) and firms.

6. Bring out the important issues on which Lucas criticizes Keynesian macroeconomics. To what extent the New-Keynesian economists have accepted these criticisms?

Ans) Keynes' General Theory was the origin for the development of macroeconomics as a branch of economics. However, the teaching of macroeconomics as a subject, especially in the United States, was based on several mathematical formalizations, which, correctly or incorrectly, were widely perceived as containing the essence of Keynes' economic doctrine. The simple Keynesian model, and the IS-LM and AS-AD models (See Block- I), provided the backbone of undergraduate macroeconomic textbooks for a very long period. These models also served as the basis for macroeconomics models, which were used in various countries to predict the impact of alternative policies on targeted macroeconomic variables.' though Keynes himself largely disapproved of the use of schnoodles hr policy evaluation. by the mid-1 960s macroeconomic policies in most industrialized economies utilized, in varying degrees, such models for policy making.

In any macroeconomic model there are certain features of the economy which arc assumed to remain constant. The whole coin plex of features that do not change is called the economic structure or simply, the model. Numerical constants characterizing the structure are called structural parameters. Characteristics of the economy which are subject to change are the variables in the model and they can be divided into two categories: endogenous and exogenous. Endogenous variables are variables whose values are sought to be explained within the model which exogenous variables are those which can be assumed to be known in advice, being determined outside the model.

Let us consider the followings simple model of income determination for illustration:

Where c: aggregate real consumption expenditure, i : aggregate real investment expenditure, y : real national income, and t : (real) revenue from direct taxes (less government transfer payments) as a proportion of national income. Here a and b are I positive constants (0 <a, b< I) which represent structural parameters, c. and y are 1 endogenous variable and i and tare exogenous variables. In (6.2) Me can say that (1-t)y is the personal disposable income.

The above is a deterministic model where the endogenous variables c and y are

entirely determined, given the values of the exogenous variables. -Since there are bvo

equations with two endogenous variables we can find out the equilibrium value of c and y

However, a deterministic model is usually used to isolate the most important determining

factors for the variables of interest; in this case, and to represent the relationships Uncertainty between the variables in the model in a simple and clear manner. These models therefore are necessarily simplified representations of reality which do not consider every factor which can affect the variables of interest. Therefore, economists accept those deterministic equations (such as (6.2)) will not exactly describe the relationship between endogenous variables (such as c and y) and exogenous variables (such as i and t) which is revealed by actual data.

The usual strategy, which is followed in order to relate deterministic economic models to actual data, is to separately introduce new variables in various deterministic equations of a model. The new variable(s) corresponding to each equation is supposed to encapsulate the effects of all other factors which can affect the exact relationship between variables given by that equation. 'The variables which are introduced are taken to be random variables representing random disturbances to the deterministic relationship between endogenous and exogenous variables in the model. Thus, the income determination model in (6.1 X6.2) may be modified to

where u represents an additive disturbance term introduced into the exact relationship given by (6.2). In contrast to the equation (6.2), which is deterministic, we call (6.2) a stochastic equation as the stochastic or error term 'u' is added here. No disturbance term is introduced in (6.1) because it is a definitional identity.

Equations (6.1) and (6.2') represent a very simple macro econometric model, once the

variables are all dated (that is, it is specified whether these variables all correspond to

the same time period or whether lagged values of some variables should be taken) and

assumptions about the probability distribution of u are specified. Actual

macro econometric models which are used for policy analysis in real economies ate, of

course, much larger, including many more variables and equations. For example, even

the classic macro econometric model for the United States developed by L. R. Klein

and A. S. Goldberger in 1955, had twenty stochastic equations, twenty endogenous

variables and 4ghteen exogenous variables.

In the simple income-determination model we considered above, t is a policy variable. If we assume that the random variable u is distributed with expected value 0, then from (6.1 ) and (6.2') it follow$ that the expected value of (given the values of i and t) is given by

E(v) = (i + b)l{l - a(1- t))

In order to evaluate (assuming that i is known in advance) the impact of alternative choices oft on the expected value of national income y in an economy, one needs to obtain estimates for the structural parameters a and b for the economy. This can be done through statistically estimating the parameters in the model using past data on the variables in the model.

Broadly speaking, the statistical estimate of a gives us 'an estimate of the average change in aggregate consumption expenditure, which, in the past, has been associated with a unit change in disposable income in the economy. Note that theories of consumption like the life cycle or the permanent-income theories imply that consumption expenditure in the economy depends not only on current Rational Expectations disposable income but also on expected future levels of disposable income.  disposable income depend in turn on expected future values of the variable t. The way consumption expenditure reacts to changes in current tax rates and I disposable income in a particular instance therefore depends crucially on how expected values of tax rates and disposable income change in response to changes in current values.

 Therefore, the statistical estimate of a derived from data for a particular time period 1 tells us how consumption expenditure could be expected to change following a change in tax rates and disposable income, but only in a context where current changes in tax rates would have the same kind of impact on future expectations of tax rates as in the period fiom which the data is taken.

7. Write short notes on the following.

i) Rational expectations and adaptive expectations

Ans) Adaptive expectations allow us to measure expected and actual variables, but due to their limitations, they are not as common in macroeconomics as rational expectations. The adaptive model has been simplified because it assumes that people base their decisions on data from the past.

Rational expectations are based on historical data, while adaptive expectations are based on real-time data. A rational expectation perspective expects changes to occur very slowly, while an adaptive expectation perspective tends to expect rapid changes.

n economics, adaptive expectations are a hypothetical process in which people form their expectations about what will happen in the future based on what has happened in the past. For example, if inflation is higher than expected, people revise their future expectations.

Adaptive Expectations: This is the case when you predict the future values ​​of a variable using only the past values ​​of the variable. Rational Expectations: Here, predictions for future values ​​are made using all available information.

Rational expectation theory is a widely used concept and modeling technique in macroeconomics. The theory assumes that individuals base their decisions on three main factors: their human rationality, the information they have, and their past experiences.

ii) Non-accelerating Inflation Rate of Unemployment

Ans) The non-accelerating inflation rate of unemployment (NAIRU) is the specific level of unemployment that is evident in an economy that does not cause inflation to increase. In other words, if unemployment is at the NAIRU level, inflation is constant. NAIRU often represents the equilibrium between the state of the economy and the labor market.

1. The non-accelerating inflation rate of unemployment (NAIRU) is the lowest level of unemployment that can occur in the economy before inflation starts to inch higher.

2. When unemployment is at the NAIRU level, inflation is steady; when unemployment rises, inflation decreases; when unemployment drops, inflation increases.

3. With no set formula to determine NAIRU, the Federal Reserve has historically used statistical models to put the NAIRU level somewhere between 5% and 6% unemployment.

4. Assessing the NAIRU level amid its inquiry into inflation and unemployment helps the Federal Reserve in its goal to both achieve maximum employment and price stability

5. On the downside, NAIRU does not account for the variety of factors that impact unemployment, besides inflation; also, the historical connection between inflation and unemployment can break down, rendering NAIRU less effective.