Notes on The Global Economy, by NYU Stern Department of Economics and other lecture notes for the MSQM Global Economy course

Lesson 1: How do we measure the economy?

All approaches to measuring GDP yield the same result

GDP: 3 views

GDP can be viewed as the total value of production, the total income earned by labor and capital, or the total expenditure on final goods and services. All three perspectives should yield the same result, giving us 3 different methods to measure the economy.

Production (Value Added)

Sum of value added by all firms in the economy. Each stage in the production of a good is value added. Value added is the increase in the value of a good or service at each stage of production, calculated by subtracting the cost of intermediate goods from the value of the output. This method avoids double-counting and accurately reflect the contribution of each firm to the economy’s total output.

Subtract intermediate goods/material input costs (raw materials or parts purchased)

\[ \text{value added} = \text{Sales} - \text{Material input costs} \]

Value added calculation: a firm’s value added is calculated by subtracting the cost of intermediate goods and services from its total sales revenue. This represents the value the firm has added to the products it uses in production.
Summing value added: to get the GDP for the entire economy, the value added of every production unit is added together
Final goods: GDP can also be calculated by only counting the value of final goods and services produced in the economy and excluding intermediate products, as their value is already included in the final product.

Int’l considerations

When comparing GDP for countries, we consider the market prices to determine whether a good is more valuable than another.

Political climate/structure: Countries whose society does not allow for market forces make it hard to calulate GDP (example: North Korea)

Non-market activities: not valued in the national accounts (ex. washing your own clothes and “bads” such as pollution)

Example (salmon value chain)

A fisherman catches a salmon and sells it to a smokehouse for $5. After smoking it, the smokehouse sells it to Fairway for $10, which, in turn, sells it to a restaurant for $15. The same restaurant buys lettuce from a farmer at Union Square for $3. The restaurant puts the lettuce and salmon together on a plate and sells it to an NYU student for $25. How much does each production unit contribute to GDP? What is the overall contribution to GDP?

Answer: The contributions (value added) are $5 each for the fisherman, smokehouse, and Fairway, $3 for the farmer, and $7 for the restaurant, for a total of $25.

fisher <- 5 # fisherman catches and sells to smokehouse for $5 (+$5 value)
smokehouse <- 10 # sold for $10 (added $5 in value)
fairway <- 15 # sold for 15 (added $5 in value)
salmon <- fisher + (smokehouse-fisher) + (fairway - smokehouse)

farmer <- 3 # sells lettuce for $3 (adds $3 in value)
lettuce.salmon <- farmer + salmon
restaurant <- 25 # sells lettuce + salmon for $25 ($3 + $15 = $18; $25-$18 = $7)
GDP <- salmon + farmer + (restaurant - lettuce.salmon)

salmon

## [1] 15

farmer

## [1] 3

lettuce.salmon

## [1] 18

Fisherman catches a salmon, and sells to smokehouse for $5
- Fisherman added $5 in value (did not have any costs)
Smokehouse then sells the smoked salmon to Fairway for $10
- Smokehouse added $5 in value ($10 - cost of fish)
Fairway sells to restaurant for $15
- Fairway added $5 in value ($15 - cost of smoked salmon)
Farmer sells lettuce and sells to restaurant for $3
- Farmer added $3 in value (did not have any costs)
Restaurant takes salmon + lettuce they bought and sells for $25
- Restaurant added $7 in value ($25 - cost of salmon and lettuce)
Total contribution to GDP = sum of all value added
- $5 + $5 + $5 + $3 + $7 = $25

Example (Bicycle)

Income

GDP as payments to factors measures all of the payments that ago to labor, land, and capital for producing a good. This approach yields the same result as calculating GDP as value added

Identity: GDP = Income

(payments to labor and capital, gross of depreciation)

\[ \text{Gross Domestic Product} = \text{Gross Domestic Income}\\ \text{GDP} = \text{GDI}\\ \begin{align} \text{value added during production}&=\text{sum of payments made to [labor] and [capital]}\\ &= \text{[wages] + [profits, interest, and depreciation]} \end{align} \]

The income identity means that a country’s total output (GDP) is equivalent to the total income (GDI) generated from that production.

Value add during production is the same as the sum of payments made to capital
Payments to labor: wages
Payments to capital: profits, interest, and depreciation

Capital refers to the money and assets used in the production process. Payments to capital are the various forms of income that arise from the use of capital in production and include net income (or profit), interest income, and depreciation.

It is important to distinguish capital payments from costs of productions, which are payments for intermediate goods, and which are not considered payments to capital.

GDP as Payment to Factors

Measures all of the payments that go to labor, land, and capital for producing a good.

\[ \begin{align} \text{payment to factors}&=\text{[wages]}+\text{[rent]} + \text{[profits]} +\text{[interest]}\\ &=\sum\text{(factor payments earned by all households in economy)} \end{align} \]

Example (Bicycle payment to factors)

Expenditures

Records the purchase of the final good by a household, firm, or gov’t. To calculate, use the basic national accounting formula to add the value of the final goods and services purchased.

Identity: GDP = Expenditures

(purchases of goods)

Everything produced is sold–to someone. Whatever is not sold is enveloped into I.

C: personal/household consumption

I: accumulation of capital by firms; spending on plants, equipment, and services by firms

G: Spending by federal, state, and local governments

NX: exports MINUS imports

\[ \begin{align} \text{Gross Domestic Product} &= \text{Gross Domestic Expenditure}\\ \text{GDP} &= \text{GDE}\\ &=C+I+G+NX\\ &=\text{Consumer expenditure}+\text{business and residential Investment}+\text{Gov't purchases}+\text{Net Exports} \end{align} \]

National Accounting Formula

$Y=C+I+G+(X-M)$

Subtract gov’t spending (taken in taxes)
$Y -G =C+I+(X-M)$

Subtract consumption
$Y-C-G=I+(X-M)$ Remaining is investment and [exports]-[imports]

National savings rate
$S=Y-C-G=I+(X-M)$

Whatever is not consumed or paid in taxes is saved

Whenever something is sold, it becomes someone else’s income

Government savings ($S_g$)

taxes = gov’t spending
taxes < gov’t spending | deficit/negative gov’t savings
taxes > gov’t spending | surplus

Trade deficit: Use when national savings rate low, and gov’t savings rate negative, the only source of funding available comes from foreigners; investment must be funded by capital inflows by means of a trade deficit; buy goods from foreigners and give them US dollars. If they don’t use the money given, they can lend it back to us.

Options to close deficit: raise taxes, cut gov’t programs, encourage savings

Consumer Price Index (CPI)

We use CPI to translate nominal into real values in the world around us everyday. It’s a tool to compare prices across years. We index or adjust future payments based on the CPI. For example, the US gov’t adjusts social security payments based on the CPI

Example: Friend’s wages

Suppose a friend’s wage is $50/hr today, the base year for our hypothetical CPI. 10 years later, they report that their nominal wage has risen to $55/hr, but the CPI has increased from 100 to 120. What is their real wage?

\[ \begin{align} \text{Real wage }&= \frac{\text{Nominal Wage}}{\text{CPI value}}\times 100\\ &=\frac{55}{120}\times 100\\ &=45.83 \end{align} \]

Salary increased by 10% but price level increased by 20%! The real wage fell.

Another example: US prices In the US, the CPI base year is commonly set to 1982-1984. The CPI rose from 100 to about 260 at the start of 2020. How much did prices rise from 1982 to 2020?

\[ \begin{align} \text{Inflation rate }&= \left (\frac{\text{Current CPI}}{\text{Base CPI}}-1\right )\times100\\ &=\left (\frac{260}{100}-1\right )\times 100\\ &=160\% \end{align} \]

In everyday terms, a basket of goods that cost $100 in 1982 would cost the same consumer $260 in 2020.

Prices vs Quantities

real GDP: output in local currency units; adjusted for inflation
nominal GDP: output once overall changes in prices have been taken out; taking literal face value; not a good measure of consumption/actual growth:

price index/deflator: measure of overall level of prices

increase in price level: INFLATION
decrease in price level: deflation

CPI (Fixed basket)

Change in total cost of a basket of goods and services that is representative of a typical household’s spending habits at a given time. Gov’t sends people to stores to check the prices of all the products in the basket. The CPI is the cost of the whole basket, normalized to equal 100 at some date

Example (fish and chips)

Consider an economy with two goods, fish and chips. At date 1, we produce 10 fish and 10 chips. Fish sell for 25 cents and chips for 50 cents. At date 2, the prices of fish and chips have risen to 50 cents and 75 cents, respectively. The quantities have changed to 8 and 12.

Note that the two prices have not gone up by the same amount: the price of fish has doubled, while chip prices have gone up by only 50 percent. Another way to say the same thing is that the relative price of chips to fish has fallen from ($2=\frac{.50}{.25}$) to ($1.5=\frac{.75}{.50}$). What is the inflation rate?

fish.and.chips <- readr::read_csv("fish-and-chips.csv") |> data.frame()
attach(fish.and.chips)
fish.and.chips$CPI.value <- (price.chips*qty.chips) + (price.fish*qty.fish)
fish.and.chips$CPI.value[2] <- (price.chips[2]*qty.chips[1]) + (price.fish[2]*qty.fish[1])
fish.and.chips$nominal.GDP <- (price.chips*qty.chips) + (price.fish*qty.fish)
detach(fish.and.chips)
fish.and.chips |> knitr::kable()

Date	price.chips	qty.chips	price.fish	qty.fish	CPI.value	nominal.GDP
1	0.50	10	0.25	10	7.5	7.5
2	0.75	12	0.50	8	12.5	13.0

Nominal GDP growth: \[ \begin{align} g_{PY}&=\frac{\text{difference in nominal GDP between dates}}{\text{nominal GDP of date 1}}\\ &=\frac{13.00-7.50}{7.50}\\ &=0.733\\ &=73.3\% \end{align} \]

Inflation rate: \[ \begin{align} \pi&=\frac{12.50}{7.50}-1\\ &=0.667\\ &=66.7\% \end{align} \]

Real GDP growth: \[ \begin{align} g_Y&=\frac{1+g_{PY}}{1+\pi}-1\\ &=\frac{1+0.733}{1+0.667}-1\\ &=0.04\\ &=4\% \end{align} \]

CPI in the base year is normalized to 100 (divide each year’s CPI value by the base year’s CPI value)

attach(fish.and.chips)
fish.and.chips$CPI <- round((CPI.value/CPI.value[1])*100)
detach(fish.and.chips)
fish.and.chips |> knitr::kable()

Date	price.chips	qty.chips	price.fish	qty.fish	CPI.value	nominal.GDP	CPI
1	0.50	10	0.25	10	7.5	7.5	100
2	0.75	12	0.50	8	12.5	13.0	167

Price deflator (Fixed weight)

Over several periods, a constant set of prices are applied to changing quantities.

Example (fish and chips cont’)

fish.and.chips <- readr::read_csv("fish-and-chips.csv") |> data.frame()
attach(fish.and.chips)

fish.and.chips$nominal.GDP <- (price.chips*qty.chips) + (price.fish*qty.fish)
fish.and.chips$real.GDP <- (price.chips*qty.chips) + (price.fish*qty.fish)

fish.and.chips$real.GDP[2] <- (price.chips[1]*qty.chips[2]) + (price.fish[1]*qty.fish[2])

fish.and.chips$deflator <- fish.and.chips$nominal.GDP/fish.and.chips$real.GDP # nominal GDP/real GDP

fish.and.chips$inflation.rate <- fish.and.chips$deflator-1

detach(fish.and.chips)
fish.and.chips |> knitr::kable()

Date	price.chips	qty.chips	price.fish	qty.fish	nominal.GDP	real.GDP	deflator	inflation.rate
1	0.50	10	0.25	10	7.5	7.5	1.000	0.000
2	0.75	12	0.50	8	13.0	8.0	1.625	0.625

Other issues

Causality: There is no causality built into the identities

Underground economy: underground activity is generally not reported and, therefore does not show up in official statistics

Capital gains: They are a part of your income, but do not show up in GDP because they do not reflect (at least not directly) the production and sale of current output

GDP vs GNP: Gross National Product (GNP) measures output produced by inputs owned by the residents of that country; need to consider a country’s income paid to the country’s capital invested abroad and subtract income paid to capital installed the country but owned by citizens of other countries; it’s a measure of income received by “locally-owned” labor and capital.

Net exports vs current account: net exports plus net recipts of foreign capital and labor income plus miscellaneous transfers from abroad.

Chain weighting: method between fixed-basket and -weight methods. It addresses the problem of applying the same prices over long periods of time.

Prices and quality change

Expenditure deflating

PPP-adjusted data

Seasonal adjustment

Revisions

Inflation, Disinflation, and Deflation

Inflation

Demand-Pull Inflation

The first one I’ll call demand pull factors, conditions that are leading companies and consumers to simply demand more goods and services than the economy is able to supply. We would call this a problem of too many dollars chasing too few goods. This increase in demand could be driven by consumer optimism about the economy, for example. Another cause might be excess government stimulus or spending. For example, we saw after COVID that households which were flush with cash from government assistance, significantly increased their purchases of products. But there are simply not enough goods to go around. If there are shortages of cars, what happens? Consumers bid up the price. A related cause might be what we call expansionary or too loose monetary policy. When interest rates are low, it becomes easier for companies and households to borrow, leading to cases where demand again outstrips supply. And again, too many dollars are chasing too few goods. An extreme example of this would be governments simply printing money to pay their own bills. For example, in Zimbabwe, a government that was bankrupt printed money. Whenever a bill came due, within a few months, the country was faced with hyperinflation. A similar story played out in Germany in the 1920s.

Cost-Push Inflation

A second category driving inflation focuses on cost push inflation, or what we’ll call pass through inflation. Cost push inflation happens when something on the supply side negatively impacts the ability of companies to deliver goods and services. As the costs companies face increase, they’re forced to pass these on to their customers. We also saw that in recent years, for example, spikes in the price of oil or wheat after the war in Ukraine led to supply disruptions. Or during COVID, when supply chains for a range of goods were disrupted as well. This could also be driven by a shortage of workers. In the early 2020s, the U.S. faced a shortage of workers as some retired with the aging of the workforce. Other potential workers were sidelined with long COVID and immigration levels fell. The combination of these factors led to acute labor shortages. Companies desperate for workers bid up wages and are forced to raise prices.

Inflation Expectations

The third source of inflation is expectations of future inflation by consumers and firms. This is a more subtle but very powerful driver of inflation and one that the Federal Reserve is very concerned with. It turns out that one of the most powerful predictors of future inflation is what people think inflation will be. Why? If people expect higher prices in the future, their behavior changes. Consumers shrug off price increases. By comparison, if consumers expect inflation to be lower, they resist higher prices, be they at the checkout counter or demands for rent increases from their landlord. Accordingly, there’s a deep concern that if expectations of higher inflation get embedded in a society, future inflation gets built into the economy. This is also sometimes called structural or inertial inflation, and it can be hard to reduce inflation in such cases. Let’s go back to expectations. When economic actors assume there will be high inflation in the future, again, this gets built into future wage and price demands. We can easily see a vicious cycle where each group’s demands lead others to expect inflation and they in turn increase their demands still further. When we saw stubborn inflation above 10% in the 1970s in many countries, we saw landlords that wrote in regular 1 or 2% price increases per month for apartments in their leases. Unions demanded similar wage increases. Automatic price increases, in fact, became a part of almost all contracts and business transactions. This creates what we call a wage price spiral. Workers expect more future inflation, so they ask for higher salaries. This results in higher labor costs for firms to meet those demands. The firms are then forced to raise the prices of their goods or services, which leads to further inflation, leading workers to demand still further wage increases next period, setting off still more price increases. And such a spiral could be hard to escape.

Disinflation

The process of reducing inflation is called disinflation. Historically, disinflation has proved painful, and it usually requires a country to raise interest rates substantially and sometimes cut government spending to slow the economy. As unemployment increases, wage growth slows and the prices for goods stop increasing breaking the cycle. Unfortunately, this can mean that a country needs to see a large increase in unemployment before inflation falls, and it may take several years of slower growth before inflation returns to its old level. And the higher the level of inflation at the start of this disinflationary process, the greater the economic pain needed to reduce it. As a result, most developed countries target an inflation rate of 2%. This keeps inflation expectations low. Governments will automatically start raising rates when inflation moves much above this target, as they believe a small amount of economic pain now is better. If they allow inflation expectations to change, they believe it’s going to lead to much, much more pain in the future.

Deflation

Now, what about deflation? Deflation is the opposite of inflation. It is falling prices. And again, this is not to be confused with disinflation, which is the process of reducing inflation. Deflation is a case where average prices for goods and services in an economy are actually falling. Deflation is relatively rare, but potentially very, very dangerous. Why is deflation so dangerous? As prices fall, firms and consumers reduce spending as they know goods will only be cheaper in future. Why would you buy an apartment today if you know it’s going to be cheaper next year? An economy can easily end up in a deflationary spiral. Firms across the economy cut wages as prices for their goods fall. But these wage cuts lead households to reduce their spending. Firms must lower prices still further, forcing them to enact still more wage cuts, and the cycle continues. A big risk is that the financial sector in a country freezes up. No one wants to borrow as loans effectively become more expensive over time. Why would you borrow $1,000,000 to start a restaurant, even at a low interest rate, if you know the prices you charge customers, and hence your revenue, is going to fall each year? Relatedly, the debt burdens of firms and households in a deflationary environment grow. Say you borrow $1,000,000. If inflation in a normal economy is 2% a year, at the end of ten years, the real value of $1,000,000 in debt is actually closer to $800,000 as prices and wages cumulatively rose by over 20% over those ten years. But with deflation of 2% a year, that $1 million effectively grows. Your debt burden effectively increases, and it’s harder for borrowers to repay their loans. Let’s look at it from the perspective of a bank with deflation, Interest rates may be close to zero. For banks, their money becomes more valuable, just leaving it in their vault every night. Why take the risk of lending it out to someone at an interest rate close to zero if there’s even a small risk the borrower will be unable to repay their loan? Companies change their behavior in a deflationary environment too. Firms may feel they’re unable to raise prices, even in cases where individual raw materials or other costs in the industry are rising. Companies become incredibly reluctant to invest in factories or other facilities, and they’re especially fearful of raising wages because it’s hard to cut them in the future. Firms just never know if they’re going to be able to increase the prices for their products in the future. Let’s look at asset prices. With deflation, the price of stocks, real estate and other assets falls in nominal terms over time. This hurts the wealth of households and hurts consumer confidence, leading to lower spending. Japan is probably our only modern case of deflation. It suffered a collapse of both real estate and stock market bubbles in the late 1980s. This started a prolonged period of falling prices and anemic economic growth. Looking at the data, the price level in Japan in 2017 was essentially at the same level as 1997. Given all these risks, economists argue governments need to act aggressively at the first sign of potential deflation.

A final factor to discuss is core versus noncore CPI measures. Food and energy prices are included in the Consumer Price Index. These are important components. Households spend a significant portion of their income every month on food and energy, but their prices are simply much more volatile than those of other goods and services in the economy. So it’s harder to base monetary policy on inflation rates that include prices at grocery stores and the gas pump. As a result, we often use a measure called core CPI that excludes food and energy. This allows us to have a little bit less noise in the data. If changes in food and energy prices are longer lasting, they’ll eventually impact the prices of other goods in this core CPI and get picked up in the data. But as changes in food and energy prices are actually often transitory, it’s arguably better to exclude them. Looking at a simple graph, we can see that the CPI is much less volatile. If you exclude food and energy prices, which makes it easier to assess trends in inflation.

Unemployment

Types

Frictional: transaction costs of changing jobs or entering a market. Experienced by people between jobs, or entering/reentering the labor market

Structural: The different labor laws and features of an economy that may lead to a mismatch between the supplu and demand for labor.

Cyclical: Arises from the c

Unemployment rate

\[ \frac{\text{Number of unemployed workers}}{\text{Labor force}} \]

Labor Force Participation Rate (LFPR)

Evolves over time

\[ \frac{\text{Labor force}}{\text{Population aged 16 or older}} \]

Employment to Population Ratio (EPR)

\[ \frac{\text{Number of employed workers}}{\text{Population aged 16 or older}} \]

U5 & U6

Broader measures of employment to the unemployment rate

marginally attached workers: people neither working nor looking for work but indicate that they are available for a job and have looked for work sometime in the recent past

Includes discouraged workers: give a job-market related reason for not looking currently for a job

part time f.e.r.*: employed part time for economic reasons; want and available for full-time work but have had to settle for a part-time schedule

U5

\[ \frac{\text{unemployed + marginally attached workers}}{\text{labor force + marginally attached workers}} \]

U6

\[ \frac{\text{unemployed + marginally attached workers + part time f.e.r.}}{\text{labor force + marginally attached workers}} \]

Lesson 2: How do economies grow in the long run?

The Cobb-Douglass Framework

Use this framework to explain where GDP comes from

\[ Y=AK^\alpha L^{1-\alpha} \]

\[ \begin{align} Y&= \text{output}\\ A&= \text{TFP: all residual sources of growth (e.g. ideas, tech)}\\ K&=\text{equipment/infrastructure}\\ L&= \text{labor: quantity of labor}\\ \alpha&= \text{value of 0-1; extent of contribution to output}\\ &=\frac{1}{3} \text{ in the US}\\ K^\alpha&=\text{Capital contributes } \alpha \text{ to output}\\ L^{(1-\alpha)}&= \text{labor contributes }(1-\alpha) \text{ to output} \end{align} \]

With human capital (H): \[ Y=AF(K,HL)\\ H=S =\text{exp}(\sigma S) \]

with hours (h):

\[ Y=AK^\alpha (hHL) \]

Confirming that Cobb-Douglass meet function properties

More input = more output

\[ \begin{align} \frac{\partial Y}{\partial \color{red}{K}}&=A\times L^{1-\alpha}\times \alpha \times K^{\alpha-1}\\ &=\alpha\times A\times \color{blue}{K^{\alpha-1}} \times L^{1-\alpha}\\ &=\alpha\times A\times \color{blue}{K^\alpha\times K^{-1}} \times L^{1-\alpha}\\ &=\alpha \times AK^\alpha L^{1-\alpha}\times \frac{1}{K}\\ &=\alpha\times\frac{Y}{K}\\ &\rightarrow \text{positive} \end{align} \]

\[ \begin{align} \frac{\partial Y}{\partial \color{red}{L}}&=A \times K^\alpha \times (1-\alpha)L^{-\alpha}\\ &=(1-\alpha)\times A\times K^\alpha \times\frac{L}{L}\times L^{-\alpha}\\ &=(1-\alpha)\times AK^\alpha L^{1-\alpha}\times \frac{1}{L}\\ &=(1-\alpha)\times \frac{Y}{L}\\ &\rightarrow \text{positive} \end{align} \]

Both are POSITIVE, indicating positive relationship

Diminishing marginal products

\[ \begin{align} Y&=AK^\alpha L^{1-\alpha}\\ \frac{\partial Y}{\partial \color{red}{K}}&=\alpha\times\frac{Y}{K}\\ \frac{\partial ^2 Y}{\partial \color{red}{K}^2}&=\alpha\times Y \times (-1) \times K^{-2}\\ &\rightarrow \text{negative} \end{align} \]

\[ \begin{align} Y&=AK^\alpha L^{1-\alpha}\\ \frac{\partial Y}{\partial \color{red}{L}}&=(1-\alpha)\times \frac{Y}{L}\\ \frac{\partial ^2 Y}{\partial \color{red}{L}^2}&=(1-\alpha)\times Y \times (-1) \times L^{-2}\\ &\rightarrow \text{negative} \end{align} \]

Both are NEGATIVE, indicating that both are decreasing.

Constant returns to scale If we multiply both inputs by $\lambda$:

\[ \begin{align} A(\lambda K)^\alpha(\lambda L)^{1-\alpha}=\lambda\times AK^\alpha L^{1-\alpha} \end{align} \]

Production function

\[ \begin{align} Y&=AF(K,L)\\ \text{real GDP (output)}&= \text{[total factor productivity]([physical capital used in production], [labor])} \end{align} \]

More input = more output

Marginal products of capital and labor are positive (nothing “cancels” out)

\[ \frac{\partial Y}{\partial K}\color{red}{>}0,\frac{\partial Y}{\partial L}\color{red}{>}0 \]

Diminishing marginal products

Increasing in capital & labor leads to increases in output BUT does so at a decreasing rate

\[ \frac{\partial ^2 Y}{\partial K^2}\color{red}{<}0,\frac{\partial ^2 Y}{\partial L^2}\color{red}{<}0 \]

Constant returns to scale

If we multiply inputs by the same number $\lambda>0$, then we multiply output by the same amount. There is no inherent advantage or disadvantage of size

\[ AF(\lambda K, \lambda L)= \lambda AF(K,L) \]

Capital input/stock (K)

Measure of total amount of physical capital used in production

Changing capital: Capital increases with investment (new plants, equipment, etc) and decreases with depreciation (on average capital stock depreciates about 6% annually, specifically on structures and equipment which depreciate more slowly and more quickly, respectively).

\[ K_{t+1}=K_t - \delta_t K_t + I_t\\ \delta_t=\text{rate of depreciation between } t \text{ and } t+1 \]

Quality: consider that the capital could build in quality thus should count for more capital. The national income and product accountants consider changes in quality when they divide investment into price and quantity components. Lately, there’s been a sharp decrease in the price of investment goods (particularly equipment) s.t. a given dollar expenditure results in greater additions to capital.

Wars and natural disasters: these do impact capital stock, but the impact is not that concerning

Land: Land doesn’t count; it isn’t as important as more productive fixtures like plants and equipment.

Intangibles: Investments on R&D, patents, brands, and databases are not included, mostly for practical reasons.

Labor (L)

Most ideal number is simply the number of people employed (L). It can also be product of quality of labor (“human capital” H) and hours worked (h). If both is included, then labor input is $hHL$.

$H$ can equal average years of school
$H$ can credit each year of school with a given % increase in skill: $H=\text{exp}(\sigma S)$, where $\sigma$ is the extra value of a year of school. Starting point is 7% increase yearly (every year of school increases human capital by 7%)

Productivity (A/TFP)

\[ \begin{align} \text{average product of labor: }& \frac{Y}{L}\\ \text{marginal product of labor: }& \frac{\partial Y}{\partial L}\\ \text{total factor productivity: }& \frac{Y}{F}(K,L) \end{align} \]

For Cobb-Douglas:

\[ \begin{align} \text{average product of labor: }& A\left (\frac{K}{L}\right )^\alpha\\ \text{marginal product of labor: }& (1-\alpha)A\left (\frac{K}{L}\right )^\alpha\\ \text{total factor productivity: }& A \end{align} \]

Holding $A$ constant, the average product of labor and marginal product of labor INCREASES when ratio of capital to labor increases. (More productive if there’s more equipment to work with).

TFP attempts to measure productivity independently of the amount of capital each worker has. TFP quantifies how well an economy uses its resources, regardless of the specific amounts of capital or labor available. Anything that leads the same inputs to produce more output results in higher TFP (innovation, security, competition, anything that affects the allocation of resources can have an impact on total factor productivity)

Marginal products

Workers ar emore productive, at the margin, if TFP is high and if they have more capital to work with.

Story of Growth

Intro

10,000 years ago humanity lived in caves.
1,000 years ago life expectancy was still around 20, the vast majority of humanity lived in poverty and we needed 98% of the population just to work growing our food.
Today global life expectancy is in the 60s and we take it for granted that food will be on the table for most of humanity.

Angus Madison’s study

Year 1 AD: GDP per capita for the world was $467, above a dollar a day by today’s standards. Absolute grinding poverty by any definition.

1820: GDP had actually gone up by about 50%.

1820 - 2008: the population of the world went from one billion to almost seven billion and GDP per capita grew over tenfold from around $650 per person to around $7,500.

The hockey stick

The sudden jump in global life expectancy is often called the hockey stick.

Human life expectancy: 25 years for most of recorded history, jumped over 60 years today, and >80 in wealthier states

Quality of life increase: shot up due first to commercial and agricultural revolutions that would eventually blossom into the industrial revolution in the 19th century.

Proportion of US work force:

< 2% works to grow our food in the U.S.
10% to 15% provides all our manufactured items,
remainder are services.

Change in Japan:

Between year zero and year 1,000 the GDP per capita went from around $400 per person per year to $42 (6% growth rate)
- Over 1,000 years, instead of working 100 backbreaking hours in the field growing rice, you merely need to work 95 hours.
In recent decades, achieved 6% growth in just six months.
- Many developing countries today can achieve more economic progress in a year than formerly took a millennia.
Its economy grew from around $670 to $22,000 per capita between 1820 and 2008.

Growth for all people in all countries:

GDP per person was about $4,000 in 1960
By around 2015 the average GDP per capita in the world had risen to $11,000
- Income for the world has basically tripled and we’ve pulled several people out of poverty in just the last few decades.

US grows slow:

In 1970 the average American worker produced about $30 an hour.
By 2010 it had jumped to $60.
- In other words output per hour had doubled in the space of about 40 years.
- An American worker today could have the same lifestyle as one in 1970, but work half the hours.
- You could live like the characters in Mad Men or the Brady Bunch, but only need to work 2.5 days per week.

Insights

Declining returns: adding ONLY capital or ONLY labor, holding the other variable constant
Developing countries: initial jump in growth comes from creating capital (giving better tools, learning new skills, etc), but it doesn’t apply in developed countries
- Note: as workers learn, productivity increases (human capital)
Developed countries: employs as much capital as needed and education is already high; increase in output comes from learning to produce more with the same workers and the same money to invest it in equipment
- $L^{1-\alpha}$: labor supply changes by 0.5% in a typical year, so it can be treated as fixed
- $K^\alpha$: If we add capital, while keeping labor constant, we know this leads to diminishing returns
- $A: \text{ }\therefore$ long-term growth must come from increases in TFP
TFP: long-term growth comes from increases in total factor productivity

The Solow Model

Diminishing returns to capital means that add’l captial generates smaller and smaller additions to output.

The Solow model connects saving and investment with economic growth; the model bases growth on saving and investment
In the Solow model without productivity (TFP) growth, capital accumulation does not generate long-run growth. The reason is diminishing returns to capital: the impact of add’l capital declines the more you have. As a result, differences in saving rates have only modest effects on output per worker and nona t all on its long-run growth rate.
- Savaing affects steady-state GDP per worker, but not its growth rate. IN this sense and others, saving is secondary to long-term economic performance
TFP grown generates long-run growth in output per worker; fast-growing countries must invest more to maintain the same capital-output ratio

Model (4 equations)

\[ \begin{align} Y_t =& A_t F (K_t, L_t)\\ =&A_tK_t^\alpha L_t^{1-\alpha}\\ S_t =& I_t\\ S_t =& sY_t\\ K_{t+1}=& (1-\delta)K_t+I_t \end{align} \]

$T_t$

Changes in output come from changes in TFP capital, andlabor
Remember: one of the properties of this production function is diminishing returns to capital–each add’l unit of capital leads to a smaller addition to output

$S_t = I_t$

Remember: flow identity $S=I+NX$ linked saving to investment and net exports
Solow ruled out $NX$, therefore leaving $S_t=I_t$
Expenditure identity plays a role: ignoring gov’t expenditure (or treating it as part of consumption for the moment), this is $Y=C+I$

$S_t=sY_t$

Description of saving behavior; people save a constant fraction $s$ of their income where $s$ is between 0 and 1

$K_{t+1}$

Capital stock depreciates at a constant rate $\delta$, where depreciation rate $\delta$ is between 0 and 1

Capital dynamics

Example

Let $L=100$, $A=1$, $s=0.2$, $\delta = 0.1$, and $\alpha = \frac{1}{3}$. If the initial capital stock is 250, we can compute future values of the capital stock by applying the capital stock equation repeatedly. We then compute output from the capital stock using the production function.

Insight: Will output increase forever? No. This tells use saving and capital formation can’t be the reason that some countries grow faster than others (for this model anyway)

Saving tends to increase the capital stock by financing new investment
depreciation tends to reduce it

# Given values
L <- 100
A <- 1
s <- .2
delta <- .1
alpha <- 1/3
initial_K <- 250

# Build preliminary data frame
t <- c(0:10)
cap_dynamics <- data.frame(t)
cap_dynamics[1,2] <- initial_K 
colnames(cap_dynamics)[2] <- "K"

# Populate "K" column
for (i in 2:11) {
  cap_dynamics[i,2] <- ((1-delta)*(cap_dynamics[i-1,2]))+(s*A*cap_dynamics[i-1,2]^alpha*L^(1-alpha))
  cap_dynamics[i,2] <- cap_dynamics[i,2] |> round(1)
}

# Populate "Y" column
for (i in 1:11){
  cap_dynamics[i,3] <- A*(cap_dynamics[i,2]^alpha)*(L^(1-alpha))
  cap_dynamics[i,3] <- cap_dynamics[i,3] |> round(1)
}
colnames(cap_dynamics)[3] <- "Y"
cap_dynamics |> gt::gt()

t	K	Y
0	250.0	135.7
1	252.1	136.1
2	254.1	136.5
3	256.0	136.8
4	257.8	137.1
5	259.4	137.4
6	260.9	137.7
7	262.3	137.9
8	263.7	138.2
9	265.0	138.4
10	266.2	138.6

Sources of Economic Growth

Level and growth accounting allow us to quantify the sources of growth: the contributions of capital, labor, and total factor productivity (TFP) to growth in real GDP
TFP accounts for most of the cross-country differences in output per worker and in differences in the growth rate of output per worker

Glossary

Term	Definition	Lesson
Accessions	The act of individuals taking new jobs, irrespective of their previous employment status.	1.3
Adult Population	The total number of people in a specified geographic area who are above a certain age (often 16 or older).	1.3
Capital Gains	Profits from the sale of assets, such as stocks or real estate.	1.2
Chain-Weighting	A method of calculating a price index that uses a changing basket of goods and services, updating weights based on the previous period.	1.2
Cobb-Douglas Production Function	A specific type of production function that relates inputs (such as capital and labor) to output using exponents representing their shares. (Y = AK^αL^1-α)	1.3
Cobb-Douglas Production Function	A specific functional form of a production function, typically written as Y = AK^αL^(1-α), widely used in economics due to its properties and ability to be estimated from economic data.	2.1
Constant Returns to Scale	A property of a production function where if all inputs are multiplied by a factor, output is multiplied by the same factor, implying no inherent advantage or disadvantage of size.	2.1
Consumer Price Index (CPI)	A measure of the average change over time in the prices paid by urban consumers for a basket of goods and services.	1.2
Consumption (C)	Household spending on goods and services.	1.1
Core CPI	A measure of the Consumer Price Index that excludes volatile food and energy prices.	1.2
Cost-Push Inflation	Inflation caused by increases in the costs of production, such as wages or raw materials.	1.2
Current Account	Net exports plus net receipts of foreign capital and labor income plus miscellaneous transfers from abroad.	1.2
Deflation	A general decrease in the prices of goods and services in an economy over a period of time.	1.2
Demand for Labor	The quantity of labor firms are willing and able to hire at various wage rates, generally decreasing as wages increase due to diminishing returns.	1.3
Demand-Pull Inflation	Inflation caused by excess demand in an economy, where too many dollars are chasing too few goods.	1.2
Diminishing Marginal Product	The property where the additional output gained from increasing one input (either labor or capital), while holding other inputs constant, decreases with each additional unit of the input.	2.1
Disinflation	A slowing down in the rate of inflation.	1.2
Employed	A state of having a job or being engaged in paid work.	1.3
Employment Rate	The ratio of the number of employed individuals to the total adult population.	1.3
Expenditure Identity	The equation Y = C + I + G + NX, which states that total output (GDP) is equal to the sum of consumption, investment, government purchases, and net exports.	1.1
Fixed-Basket Approach	A method of calculating a price index using a constant basket of goods and services from a base year.	1.2
Fixed-Weight Approach	A method of calculating a price index by using constant prices from a base year to value changing quantities.	1.2
GDP Deflator	A price index that measures the ratio of nominal GDP to real GDP, reflecting the overall price level in an economy.	1.2
Government Purchases (G)	Spending by federal, state, and local governments on goods and services.	1.1
Gross Domestic Income (GDI)	The total income earned by all factors of production (labor and capital) within a country’s borders; should equal the value of the output produced, GDP.	1.1
Gross Domestic Product (GDP)	The total value of all final goods and services produced within a country's borders in a specific period, usually a year or a quarter.	1.1
Gross National Product (GNP)	The total value of output produced by the residents of a country, regardless of where the production takes place.	1.2
Human Capital	The skills, knowledge, and experience possessed by individuals or the labor force, often measured by education and other indicators of workforce quality.	2.1
Inactive/Not in the Labor Force	People who are neither employed nor actively seeking employment.	1.3
Inflation	A general increase in the prices of goods and services in an economy over a period of time.	1.2
Investment (I)	Spending by firms and households on new capital goods, including machinery, equipment, buildings, and changes in inventories.	1.1
Job Creation	The phenomenon of the creation of new job positions by either expanding existing firms or new firms hiring workers.	1.3
Job Destruction	The process of eliminating job positions by firms.	1.3
Job Reallocation (or Job Turnover)	The combined processes of job creation and destruction, reflecting the shifting of employment between different sectors or firms.	1.3
Labor Force	The sum of individuals who are either employed or unemployed (actively seeking work).	1.3
Labor Input (L)	The quantity of labor used in production, typically measured as the number of employed people, possibly adjusted for skill or hours worked.	2.1
Labor Market	The market where workers find jobs and employers seek workers.	1.3
Marginal Product of Capital (MPK)	The additional output that is generated by an additional unit of capital, holding other inputs constant.	2.1
Marginal Product of Labor (MPL)	The additional output that is generated by an additional unit of labor, holding other inputs constant.	2.1
Minimum Wage	A government-mandated minimum hourly wage that employers are required to pay their workers.	1.3
National Income and Product Accounts (NIPA)	A system of macroeconomic accounting that provides comprehensive information about the production, income, and expenditures of an economy.	1.1
Net Exports	The value of a country’s exports minus the value of its imports.	1.2
Net Exports (NX)	The value of a country's exports minus the value of its imports.	1.1
Nominal GDP	The value of output calculated using current prices, meaning no adjustments have been made for inflation.	1.1
Nominal GDP	The total value of goods and services produced in an economy at current market prices, not adjusted for inflation.	1.2
Participation Rate	The ratio of the labor force to the total adult population.	1.3
Physical Capital (K)	The stock of plant, equipment, and infrastructure used to produce goods and services; typically measured in monetary terms by valuing different kinds of capital at base-year prices.	2.1
PPP-Adjusted Data	Economic data adjusted for purchasing power parity, which accounts for differences in price levels across countries.	1.2
Price Index/Deflator	A measure of the overall level of prices, used to track inflation and adjust nominal values to real values.	1.1
Production Function	A mathematical relationship that describes how inputs (such as capital and labor) are transformed into output (such as real GDP).	2.1
Productivity (TFP)	Total factor productivity is a measure of the overall efficiency of an economy in transforming inputs into outputs, representing the portion of output not explained by changes in capital and labor.	2.1
Real GDP	A measure of output adjusted for changes in price levels over time, using prices from a base year; gives the quantity of output produced in a particular period.	1.1
Real GDP	The total value of goods and services produced in an economy, adjusted for inflation to measure the actual quantity of output.	1.2
Reservation Wage	The lowest wage rate at which an individual is willing to accept employment; the value they place on their time not spent working.	1.3
Saving (S)	The portion of income that is not consumed, and therefore is available for use by others as financing.	1.1
Seasonal Adjustment	A statistical technique to remove predictable seasonal variations from economic data.	1.2
Separations	The act of individuals leaving jobs for any reason, irrespective of their next destination.	1.3
Speed of Adjustment Parameter (λ)	A parameter in the unemployment dynamics model that describes how quickly the unemployment rate returns to its steady-state value after a shock. (λ = 1 - (s+a) where 's' is the separation rate and 'a' is the accession rate)	1.3
Supply of Labor	The quantity of labor individuals are willing and able to offer at various wage rates, generally increasing as wages increase.	1.3
Underground Economy	Economic activity that is not officially recorded or reported in official statistics.	1.2
Unemployed	The state of not being employed but being actively seeking employment.	1.3
Unemployment Rate	The ratio of the number of unemployed individuals to the total labor force.	1.3
Value Added	The increase in the value of a good or service at each stage of production, calculated as the difference between the value of output and the cost of intermediate goods.	1.1
Value-Added	The increase in the value of a product at each stage of production, calculated by subtracting the cost of inputs from the value of outputs.	1.2
Wage-Price Spiral	A cycle in which rising wages lead to higher prices, which in turn lead to demands for further wage increases.	1.2

Global Economy

Sammy Amos

2025-01-13