Investment in the Long and Short Run: Macroeconomics and Loanable Funds

Macroeconomic Investment Fundamentals

Definition of Investment in Macroeconomics
- Investment is defined as the up-front cost incurred in acquiring inputs today in the hope of receiving future output benefits.
- Investment represents a flow variable: the purchase of new capital over a specific period, which increases the overall productive capacity of the economy.
- Capital represents a stock variable: the physical and non-physical assets (such as machinery, building structures, and intellectual property) currently available and used to produce output.
- Macroeconomic investment specifically involves purchases of:
  - Equipment: New machinery, computers, tools, company vehicles, etc.
  - Structures: New factories, office buildings, retail stores, and major remodeling of existing facilities.
  - Research and Development: Expenditures on software development, scientific R&D, and literary, television, movie, or music production.
Macroeconomic Investment vs. Conversational Usage
- In everyday conversation, the term "investment" is often used to describe actions such as:
  - Buying an existing house.
  - Paying for personal education.
  - Purchasing stocks, bonds, or shares in financial markets.
  - Depositing money into a bank account.
- These everyday activities do not constitute macroeconomic investment because they do not involve the creation or purchase of new physical capital assets or increase the productive capacity of the economy. Buying an existing asset is simply a financial transfer of ownership.
Role of Investment in Long-Term Living Standards
- Investment is a critical driver of a nation's long-term economic growth and standard of living.
- Mechanism of growth:
  - Investment made today expands the economy's stock of tools, structures, and machinery (e.g., purchasing tractors for agricultural production).
  - A larger stock of capital enables workers to produce significantly more output for every hour worked in the future (e.g., harvesting higher volumes of grain).
  - Countries with higher capital per worker produce more output per worker, serving as a primary explanation for why some nations are rich while others remain poor.
- Asset ownership division:
  - Public investment: Funding public assets such as roads, bridges, and ports.
  - Private investment: Funding business capital (machinery, software) or household structures (residential dwellings).
- Role of Depreciation: Because capital assets continuously suffer physical wear and tear or obsolescence, a major fraction of annual investment merely replaces worn-out capital and does not increase net capital per worker.
Role of Investment in Short-Term Business Cycles
- Private investment is extraordinarily volatile and experiences dramatic fluctuations year-to-year as business and household conditions change.
- Sensitivity to GDP: If GDP declines by $1\%$ , private investment can plummet by $10\%$ .
- Net Investment Volatility: Net investment—defined as total investment undertaken beyond what is required to replace depreciated capital—is particularly volatile.
- Key short-run drivers:
  - Changing future expectations of businesses and households regarding economic demand (which shift in complex, hard-to-predict ways).
  - Other broader economic developments, including shifts in real interest rates, corporate tax policies, and financial sector conditions (though these are generally less dominant as primary drivers than business expectations).
Three Types of Macroeconomic Investment
- Business Investment:
  - Money spent by commercial enterprises on new capital assets to expand productive capacity.
  - Divided into equipment (e.g., computers, company cars), structures (e.g., offices, stores, factories), and intellectual property (e.g., software, R&D, media production).
  - Depreciation of total business capital stock typically equals roughly $10\%$ of GDP annually, underlying the emphasis on Gross Domestic Product.
- Housing Investment:
  - Money spent on constructing new houses or apartments, as well as expenditure on structural improvements, alterations, and additions to existing residential properties.
  - Building a new home constitutes macroeconomic investment because it creates new physical capital capable of generating future housing services.
  - Purchasing an existing home is not macroeconomic investment because it represents a transfer of ownership without adding new capital stock.
  - Purchasing a "fixer-upper" house does not count as investment, but the subsequent spending on physical renovations and structural upgrades does.
- Inventories:
  - Stocks of raw materials, work-in-progress goods, and unsold final goods held by businesses (e.g., new vehicles parked at a dealership available for test drives).
  - An increase in inventory levels over a period is classified as investment.
  - Inventories constitute a very small percentage of total aggregate investment but exhibit extreme quarterly volatility.
  - Interpreting inventory movements is difficult: a buildup of inventories may signal an unexpected drop in consumer sales or a deliberate strategic choice by firms anticipating future demand surges.

Tools for Investment Analysis

Fundamental Trade-off in Investment Decisions
- All investment decisions hinge on comparing immediate, up-front financial costs against uncertain, future financial benefits.
- Evaluating investments requires an analytical framework capable of standardizing values realized at different points in time.
Tool One: Compounding
- Opportunity Cost: The cost of funding an investment includes the forgone interest that could have been earned by keeping money in a risk-free interest-bearing account or the interest paid to borrow funds.
- Compounding Defined: The accumulation of money over time resulting from earning interest on both the principal amount and previously accrued interest.
- Mathematical Mechanics:
  - Depositing $\\n100$ at an annual interest rate of $r = 3\%$ ( $0.03$ ):
    - After Year 1: $\\n100 + (0.03 \times \\n100) = \\n103.00$
    - After Year 2: $\\n103 + (0.03 \times \\n103) = \\n106.09$
- Compounding Formulas:
  - For 1 year: $\text{Future Value} = \text{Present Value} + (r \times \text{Present Value}) = \text{Present Value} \times (1 + r)$
  - For $t$ years: $\text{Future Value}_t = \text{Present Value} \times (1 + r)^t$
- Example Calculation:
  - Investing $\\n16\,000$ for $t = 20$ years in an equity portfolio yielding $r = 5\%$ ( $0.05$ ) annually:
  - $\text{Future Value}_{20} = \\n16\,000 \times (1 + 0.05)^{20} = \\n16\,000 \times 2.6533 = \\n42\,453$
- Core Insight: Receiving $\\n100$ at a future date is worth strictly less than receiving $\\n100$ today, because money received today can be invested immediately to generate compound interest.
Tool Two: Discounting
- Discounting Defined: The reverse of compounding, converting expected future dollar amounts into their equivalent present-day values.
- Discounting Formula:
  - $\text{Present Value} = \text{Future Value}_t \times \frac{1}{(1 + r)^t}$
- Application Scenario (Concept Check):
  - Calculating the present value of receiving $\\n20\,000$ in $t = 5$ years at a discount rate of $r = 3\%$ ( $0.03$ ) per year:
  - $\text{Present Value} = \\n20\,000 \times \frac{1}{(1 + 0.03)^5} = \\n20\,000 \times \frac{1}{1.15927} = \\n17\,252$
- Determinants of Discount Rates: The discount rate applied can represent an objective financial benchmark (such as prevailing bank interest rates over the duration) or a subjective measure of personal impatience.
Tool Three: Real vs. Nominal Interest Rates
- Nominal Values: Expressed purely in current dollar terms, using nominal interest rates to compound or discount future nominal cash flows.
- Real Values: Adjusted for inflation, using real interest rates to measure true purchasing power (the actual volume of goods and services that funds can purchase).
- Utility Impact: Real values matter far more for decision-making because individual and firm utility depends on physical purchasing power rather than nominal currency units.
- Comparative Stock Market Scenario ( $1920$ to $2020$ ):
  - An initial investment of $\\n1\,000$ in the stock market compounded at an average rate of $10\%$ per year over $100$ years.
  - a) Nominal Future Value:
    - $\text{Nominal FV}_{100} = \\n1\,000 \times (1 + 0.10)^{100} = \\n13\,780\,612$
  - b) Real Future Value (given an average inflation rate of $3.6\%$ per year):
    - Real interest rate $r_{\text{real}} = 10\% - 3.6\% = 6.4\%$ ( $0.064$ ).
    - $\text{Real FV}_{100} = \\n1\,000 \times (1 + 0.064)^{100} = \\n494\,496$
  - Conclusion: Inflation drastically reduces actual purchasing power, leaving the real future value at $\\n494\,496$ compared to the nominal figure of $\\n13\,780\,612$

Making Investment Decisions and the Rational Rule

Six-Step Recipe for Investment Evaluation
1. Compare the present value of the potential investment's future benefits directly against its up-front costs.
2. Establish that the present value of up-front costs (costs incurred today) equals the explicit up-front dollar expenditure.
3. Account for asset depreciation when forecasting future annual revenues.
4. Convert all expected future revenue streams into present value terms.
5. Pursue the investment if the aggregate present value of future benefits exceeds the present value of up-front costs (provided no alternative project offers a higher net present value).
6. Adjust decision thresholds to account for corporate risk preferences regarding return volatility.
Case Scenario: Evaluating a Wind Turbine Investment
- Background: A renewable energy company operating $8$ active wind turbines (powering nearly $15\,000$ homes) evaluates whether to purchase a $9\text{th}$ turbine.
- Up-front Cost ( $C$ ): Requires an initial outlay of $\\n4\,000\,000$ ( $\text{PV of cost} = \\n4\text{ million}$ ).
- Revenue Projections & Depreciation ( $d$ ):
  - Year 0 (construction): $\\n0$ revenue.
  - Year 1 revenue: $\\n600\,000$
  - Subsequent annual revenues decline by $d = 4\%$ ( $0.04$ ) per year due to physical depreciation:
    - Year 2 revenue: $\text{Year 1 Revenue} \times (1 - 0.04) = \\n600\,000 \times 0.96 = \\n576\,000$
    - Year 3 revenue: $\text{Year 2 Revenue} \times (1 - 0.04) = \\n576\,000 \times 0.96 = \\n552\,960$
- Present Value Calculations at an Interest Rate ( $r$ ) of $6\%$ ( $0.06$ ):
  - Present Value of Year 1 revenue: $\frac{\\n600\,000}{1 + 0.06} = \\n566\,038$
  - Perpetuity Valuation Formula Shortcut: For a depreciating revenue stream, total present value of all future revenues simplifies mathematically to:
    - $\text{Present Value of Future Revenues} = \frac{\text{Next Year's Revenue}}{r + d}$
  - Applying values: $\text{PV of Benefits} = \frac{\\n600\,000}{0.06 + 0.04} = \frac{\\n600\,000}{0.10} = \\n6\,000\,000$
- Investment Decision Outcome:
  - Present Value of Benefits = $\\n6\,000\,000$
  - Present Value of Costs = $\\n4\,000\,000$
  - Net Profit Expansion = $\\n6\,000\,000 - \\n4\,000\,000 = \\n2\,000\,000$
  - Recommendation: The company should proceed with purchasing the $9\text{th}$ turbine.
The Rational Rule for Investors
- For a risk-neutral investor, an investment opportunity should be undertaken if the present value of future revenues exceeds up-front capital costs ( $C$ ):
  - $\frac{\text{Next Year's Revenue}}{r + d} > C$
Real-World Hurdles and Risk Adjustments
- In real-world business environments, revenue forecasts and estimated depreciation rates contain uncertainty.
- Companies establish hurdle rates—required minimum internal returns—that far exceed baseline market interest rates.
- In Australia, for instance, corporate hurdle rates routinely require around a $14\%$ gross annual revenue return on capital outlays before approving project expenditures.

Macroeconomic Drivers of Investment

Impact of Real Interest Rates on Aggregate Investment
- Higher real interest rates ( $r$ ) across the macroeconomy cause managers to cut back on new capital investments.
- Opportunity Cost Principle: High market interest rates increase the opportunity cost of capital, as firms can alternatively hold money in financial assets to earn risk-free interest. Consequently, fewer capital projects yield returns high enough to pass the cost-benefit test.
- Revisiting the Wind Turbine Example across Varying Real Interest Rates ( $r$ ):
  - At $r = 6\%$ : $\text{PV of Revenue} = \frac{\\n600\,000}{0.06 + 0.04} = \\n6\,000\,000 > \\n4\,000\,000$ $\rightarrow$ Invest
  - At $r = 8\%$ : $\text{PV of Revenue} = \frac{\\n600\,000}{0.08 + 0.04} = \\n5\,000\,000 > \\n4\,000\,000$ $\rightarrow$ Invest
  - At $r = 12\%$ : $\text{PV of Revenue} = \frac{\\n600\,000}{0.12 + 0.04} = \\n3\,750\,000 < \\n4\,000\,000$ $\rightarrow$ Do NOT Invest
The Investment Line
- The investment schedule maps total macroeconomic investment relative to the prevailing real interest rate.
- Slope: Downward-sloping. As real interest rates rise, the present value of future returns falls, decreasing total project eligibility.
- Movements Along the Line: Caused exclusively by changes in the real interest rate.
  - A rise in the real interest rate leads to a movement upward along the curve, reducing investment quantity.
  - A fall in the real interest rate leads to a movement downward along the curve, increasing investment quantity.
- Empirical Sensitivity: In empirical practice, aggregate business investment is relatively insensitive to minor shifts in real interest rates due to high corporate hurdle rates ( $\approx 14\%$ ).
Four Factors that Shift the Investment Line
- A change in business conditions that raises investment profitability shifts the entire investment line to the right; conditions reducing profitability shift it to the left.
- 1. Technological Advances:
  - New technology enhances capital equipment productivity, lifting expected future output and revenues.
  - Can lower effective asset depreciation rates.
  - Shifts the investment line to the right. Integrating new technologies into business operations requires substantial implementation time (e.g., current integration of artificial intelligence).
- 2. Corporate Tax Policy:
  - Higher corporate tax rates diminish the net share of profits retained by firms, shifting the investment line left.
  - Targeted tax breaks (such as investment tax credits for renewable wind energy) boost retained returns, shifting the investment line right.
  - In practice, tax rates are less influential than a nation's underlying supporting institutional environment—including political stability, quality of governance, bureaucratic efficiency, and local supply network density.
  - Misconception Context: Public statements claiming massive growth purely from tax cuts (e.g., President Donald Trump in 2016 asserting, “Lowering business tax rates will be a substantial boom to our economic growth rate as investment will take off like a rocket.”) oversimplify investment drivers relative to institutional and market realities.
- 3. Lending Standards and Cash Reserves:
  - Financing mechanisms for investment include bank debt, stock issuance, and internal cash balances.
  - Investment line shifts to the right when financial institutions relax lending constraints, equity stock markets experience sustained bull runs, or corporate balances accumulate substantial cash reserves.
- 4. Business Expectations and Confidence:
  - Optimism regarding long-term macroeconomic demand leads managers to project robust future revenues, shifting the investment line to the right.
  - Pessimism regarding future demand drives lower revenue projections, shifting the investment line to the left.
  - High managerial confidence is essential for long-horizon capital investments with long construction timelines (such as mining projects).
  - In practice, shifts in business confidence represent the single largest driver of annual investment volatility, outweighing real interest rate changes.
Herding Behavior and Short-Run Business Cycles
- Because future economic conditions are highly uncertain, business managers frequently copy competitor behavior, resulting in herding behavior (industries synchronously expanding or halting capital investment).
- Herding dynamics make net private investment extremely volatile, serving as a primary driver of aggregate annual fluctuations in real output and GDP (the business cycle).

The Market for Loanable Funds and Secular Stagnation

Structure of the Market for Loanable Funds
- Definition: The aggregate financial market where loanable funds are supplied, borrowed, and allocated for buying, renting, or constructing capital assets.
- Determines the equilibrium long-run real interest rate and aggregate volume of loanable funds.
- Market Participants:
  - Suppliers (Savers): Households, institutions, governments, and foreign lenders offering saved funds to financial intermediaries.
  - Demanders (Investors): Businesses and households borrowing funds from financial intermediaries to finance capital investment projects.
  - Financial Intermediaries: Banks, corporate bond markets, and stock exchanges linking suppliers directly or indirectly to demanders.
  - Price of Loanable Funds: The real interest rate (the annual cost paid by borrowers per dollar borrowed).
Equilibrium in the Loanable Funds Market
- Supply Curve: Upward-sloping relative to the real interest rate, as higher rates increase financial returns on savings.
- Demand Curve: Downward-sloping relative to the real interest rate, as higher interest rates lower net present values of investment opportunities.
- Equilibrium Point: The intersection of loanable funds supply and demand determines the long-run market interest rate.
- Neutral Real Interest Rate: The theoretical equilibrium real interest rate observed when the macroeconomy is operating in neutral balance—producing output precisely at potential capacity without over-expansion or recession.
Shifts in Loanable Funds Supply
- An increase in aggregate saving shifts the supply curve right, reducing the equilibrium real interest rate.
- A decrease in aggregate saving shifts the supply curve left, elevating the equilibrium real interest rate (e.g., shifts from $2.5\%$ up to $3.0\%$ or $3.5\%$ ).
- Three key participant groups whose saving habits determine supply shifts:
  1. Private domestic savers (households).
  2. Public sector entities (state and federal government budget balances).
  3. Foreign investors and sovereign entities supplying cross-border capital.
Shifts in Loanable Funds Demand
- An increase in macroeconomic investment demand shifts the demand curve right, raising the equilibrium real interest rate (e.g., shifts from $2\%$ up to $3\%$ or $4\%$ ).
- A decline in investment demand shifts the demand curve left, driving interest rates down.
- Factors shifting loanable funds demand identical to investment shifters:
  1. Technological breakthroughs.
  2. Corporate tax legislation.
  3. Financial credit standards and firm cash reserves.
  4. Shifts in executive confidence and future demand expectations.
Secular Stagnation and Long-Run Rate Declines
- Over recent decades, global financial markets have experienced a persistent, structural decline in long-run real interest rates.
- Driven by a simultaneous expansion in global loanable funds supply and a structural contraction in investment demand.
- Four Drivers of Global Rate Declines:
  1. Demographic Aging: Slowing population growth and population aging in advanced economies, forcing households to save higher fractions of income for retirement.
  2. Emerging Market Capital Accumulation: Rapid income growth in major emerging markets (e.g., China and India) where structural household savings rates are high.
  3. Asset-Light Tech Sector Growth: Expanding dominance of technology firms requiring far less physical machinery and real infrastructure relative to traditional heavy manufacturing sectors.
  4. Cheaper Capital Goods: Falling price trends for high-tech capital equipment, particularly computers and processing hardware, reducing required dollar outlays per unit of capital.