FMI GRADUATE SEMINAR

CAPITAL THEORY

Nicolás Cachanosky
Metropolitan State University of Denver
ncachano@msudenver.edu

## Agenda

1. A history of roadblocks 2. Finance: A way out 3. ABCT 4. Financial microfoundations 5. Future areas of research

A history of roadblocks

### A HISTORY OF ROADBLOCKS

**MENGER**

Sets the stage: *Earlier* and *later* production goods

  • Consumption goods are produced by goods of various “orders”
    • Higher order goods are transformed into lower order goods
  • Structure of production
    • How to sequently order the use of production goods [period of production]
    • How to combine different production goods [heterogeneity]

### A HISTORY OF ROADBLOCKS

**MENGER**

* Economic progress * A "lengthening" of the period of production * More time and more complexity * Remember: * Theory of subjective (marginal) value * The cost of production is determined by the price of the final goods

### A HISTORY OF ROADBLOCKS

MENGER | **BÖHM-BAWERK**

Builds on Menger * Roundaboutness * How **long** and **complex** a production process is * More *roundabout* processes are chosen *only if* the output value is at least equal to the extra roundaboutness * But... once a new technology is in place, production takes **less** time * Similar to a highway in a city * Is then the **period of production** *forward* or *backward* looking?

### A HISTORY OF ROADBLOCKS

MENGER | **BÖHM-BAWERK**

The average period of production $$ \begin{align} APP &= \sum_{t=1}^{n} [\omega_t \cdot (n-t)] \\\\[10pt] APP &= \sum_{t=1}^{n} \left[ \frac{l_t}{\sum l_t} (n-t) \right] \\\\[10pt] l_t & \geq 0 \rightarrow \omega \in (0,1), \sum \omega = 1 \end{align} $$

### A HISTORY OF ROADBLOCKS

MENGER | **BÖHM-BAWERK**

The average period of production: Problems

  • Objective measure of labor
    • Did Böhm-Bawerk became a marxist?
  • Simple (rather than compounding) interest rate
  • Why lower stages carry more weight than higher stages?
  • There is no market (subjective) value
  • APP is backward looking
    • APP is either infinite or arbitrary

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | **HAYEK**

Builds on Böhm-Bawerk

  • Hayekian triangle: Context
    • Pedagogical tool
    • Not for academic research
  • Hayekian triangle: Improvement over Böhm-Bawerk
    • Horizontal-axis: Time-value
    • Vertical-axis: Market value

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | **HAYEK**

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | **HAYEK**

Remaining issues

  • Stages of production do not exist, they are subjective
  • Looping
  • Simple (not compounding) interest rate
  • Backward looking
  • Change of focus: From APP to stages of production

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | **HAYEK**

A better Hayekian triangle (for empirical research)

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | **HAYEK**

[Hayek (1941, pp. 3-4, see also pp. 92-93)](https://mises.org/library/pure-theory-capital-0) gives up on the APP

I had little idea […] that some of the simplifications employed by the earlier writers had such far-reaching consequences as to make their conceptual tools almost useless in the analysis of more complicated situations. The most important of these **inappropriate** simplifications […] was the attempt to **introduce the time factor** into the theory of capital in the form of one single relevant time interval—the ‘average period of production.’

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | **HAYEK**

If APP is not possible... then what?

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | **LACHMANN**

Focus on capital heterogeneity

  • Capital: The order in which heterogeneous goods are combined to produce specific goods
    • Capital goods are neither perfect substitutes nor perfect complements
    • Capital structure is revised as entrepreneurs think of new ways to produce goods (new -more complex- combinations)
  • Capital (good) is subjective

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | **LACHMANN**

If you take capital heterogeneity seriously

  • Aggregation is impossible
    • Capital is heterogeneous
    • Capital is subjective
    • Capital goods can have different degrees of specifity
    • The market is like a kaleidoscope (complex figures are seen different by different actors)
  • Technology
    • Capital accumulation leads to technological change

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | **LACHMANN**

Capital heterogeneity vs formal economics

  • For the kind of mathematics used in economics, homogeneous capital is easy and convenient
  • Modeling capital heterogeneity increases the complexity of the model
  • Capital heterogeneity was set aside and mathematical tractability took priority

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | **LACHMANN**

Now what?

  • Capital $\rightarrow$ roundaboutness
  • Roundaboutness
    • Period of production: roadblock!
    • Heterogeneity: roadblock!

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | **MISES**

Go back to the basics

  • What is capital?
    • View 1: Physical goods, or tools? - Adam Smith
    • View 2: Market value of all productive assets of whatever type, form, or shape - Mises
  • Aggregation
    • View 1: Needs to assume homogeneity
    • View 2: A money-value construct (financial capital)

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | **MISES**

Some word... different meanings...

  • Production function: What is $K$?
    • (1) $Q = F(A, K, N)$
  • Economic profits of the firm: What is $K$?
    • (2) $\pi = PQ - wN - rK$
  • Insert (1) into (2): What is $K$?
    • $\pi = P \cdot F(A, K, N) - wN - rK$

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | **MISES**

Financial capital depends on historical and institutional context

  • Economic calculation under socialism: $K$ does not exist
    • $\underbrace{\pi}_{\nexists} = pq - wN - r\underbrace{K}_{\nexists}$

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | MISES | **HICKS**

The forerunner

  • Hicks recognizes the role of time (production takes time)
    • A production process (or technoogy) is a stream of input and outputs (a cash-flow)
    • Inputs must precede outputs
    • Then, what conditions make a production technology profitable?

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | MISES | **HICKS**

The forerunner

  • What is the value of capital (CV)?
    • The net-present-value (NPV) of the cash-flow of inputs and outputs discounte at the cost of opportunity of the financial capital employed
    • $NPV>0$ profitable (and the other way around)

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | MISES | **HICKS**

Formalization

  • Assumptions and definitions
    • Discrete time: $t = 1, …, T$
    • Inputs: $\varphi_t = \sum_{i} w_{i,t} g_{i,t} \quad (i=1,…,m)$
    • Outputs: $q_t = \sum_{j} \varphi_{j,t} p_{j,t} \quad ( j=1,…,n)$
    • $\pi_t = q_t - \varphi_t$
    • $f = \frac{1}{1+r}; \quad r=\text{discount rate}$

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | MISES | **HICKS**

Formalization (cont...) * Capital value $$ \begin{align} CV_0 &= \pi_0 f^0 + f^1 \pi_1 + f^2 \pi_2 = \sum_{t=0}^{\infty} \pi_t f^t \\\\[5pt] CV_0 &= (q_0 - \varphi_0) + (q_1 - \varphi_1) f + (q_2 - \varphi_2) f^2 + ... \\\\[15pt] CV_0 &= \pi_0 + CV_1 \end{align} $$

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | MISES | **HICKS**

Implications

  • Hick’s treatment is forward-looking
    • Must use expectations
    • Past-data is given, future data is expected
  • Inverse relationship between $CV$ and $r$
    • Semi-elasticity: $\frac{\Delta CV/CV}{\Delta r} < 0$
    • How? Be an economist, apply the elasticity-operator (1939)
    • Similar and independent than Macaulay duration (1938)

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | MISES | **HICKS**

Böhm-Bawerk vs Hicks

Böhm-Bawerk Hicks
backward-looking forward-looking
$APP = \sum_{t=1}^{n} \left[\frac{l_t}{\sum_t l_t} (n-t) \right]$ $APP = \sum_t = \left[ \frac{f^t \pi_t}{\sum_t f^t \pi_t} t \right]$

### A HISTORY OF ROADBLOCKS

MENGER | BÖHM-BAWERK | HAYEK | LACHMANN | MISES | **HICKS**

Summary

  • Production takes time
  • But, measuring the time involved in a production process has been unsolvable
  • Production goods are heterogeneous
    • But, there is no convenient way to incorporate this into formal theory/models
  • The default is
    • Production function without time
    • What is the interest rate then?
    • The price of capital (one way route to reswitching problems)

Finance: A way out

### FINANCE: A WAY OUT

**WHY FINANCE?**

Go back to the beginning

  • Put yourself in the shoes of an investor
  • Investment decisions are decided based on free-cash-flow (FCF) evaluation
  • If a formal model is consistent, then a financial interpretation should predict the same outcome than the theory
  • Many business cycles occur through the financial markets, therefore a financial interpretation of business cycles should be useful

### FINANCE: A WAY OUT

WHY FINANCE? | **FCF**

Think like an investor

  • Let there be $n$ different projects
  • Let $FCF = NOPAT - I$
  • The expected value of each project in $t=0$ is
    • $CV_0 = \sum_{0}^{T \rightarrow \infty} = \frac{FCF_t}{(1+i)^t}$
  • Investment projects are:
    • Forward-looking
    • Measured in (expected) market values
    • Valued at the cost of opportunity

### FINANCE: A WAY OUT

WHY FINANCE? | FCF | **EVA**

Where is the financial capital?

  • Let $W$ represent the amount invested in the project
  • Then:
    • $CV_0 = \sum_{0}^{T \rightarrow \infty} = \frac{FCF_t}{(1+i)^t}$
    • do some math-magic…
    • $CV_0 = W_0 + \sum_{t=1}^{\infty} \frac{EVA_t}{(1+i)^t}$
    • $CV_0 = W_0 + \sum_{t=1}^{\infty} \frac{(ROIC_{t - i})W_{t-1}}{(1+i)^t}$
    • $CV_0 = W_0 + MVA$

### FINANCE: A WAY OUT

WHY FINANCE? | FCF | **EVA**

APP

  • Macaulay duration $(D)$ is the financial equivalent of APP
    • The average time it takes for the cash-flow to produce $1
    • $CV = W_0 + \sum_{t=1}{\infty} \frac{EVA_t}{(1+i)^t}$
    • $D = APP = \frac{\sum_{t=1}^{\infty} \frac{t \cdot EVA_t}{(1+i)^t}}{CV}$
  • Modified duration $(MD)$
    • Semi-elasticity of $CV$ with respect to $i$
    • $MD = \frac{D}{1 + YTM}$
  • In continuous time
    • $D = MD$

### FINANCE: A WAY OUT

WHY FINANCE? | FCF | **EVA**

APP (cont...)

  • What do we know?
    • $D = APP = \frac{\sum_{t=1}^{\infty} \frac{t \cdot EVA_t}{(1+i)^t}}{CV}$
    • $D$ is a finite number even if $T \rightarrow \infty$. Why?
    • Properties of $D$:
      • Forward-looking
      • A function of market values
      • Has a time variable
      • Has a financial capital variable

### FINANCE: A WAY OUT

WHY FINANCE? | FCF | **EVA**

APP (cont...)

  • What do we know? (cont…)
    • Let two projects have same $T$ but different $W$
      • $D_{HR} > D_{LR}$
    • Let two projects have same $W$ but different $T$
      • $D_{HR} > D_{LR}$

### FINANCE: A WAY OUT

WHY FINANCE? | FCF | **EVA**

Some implications

  • APP
    • Grounded in the well-known and widespread used financial concept of Macaulay duration
  • Capital intensity
    • $K/L$ is untenable
    • Capital intensity is the size of $W$

ABCT

### ABCT

FINANCIAL FRAMEWORK

Assumptions

  • Let there be two investment projects:
    • HR: High roundabout
    • LR: Low roundabout
  • In equilibrium:
    • $PV_{HR} = PV_{LR}$
    • $\frac{PV_{HR}}{PV_{LR}} = 1$

### ABCT

FINANCIAL FRAMEWORK

### ABCT

FINANCIAL FRAMEWORK

Important lesson

  • ABCT does not need to assume Cantillon effects
    • If: Cantillon effects are defined as change in relative prices of goods of any level but not the price of time $(i)$
  • Alternative
    • ABCT uses only one Cantillon effect
    • The price of time with respect to all other goods and services (of any level)

### ABCT

FINANCIAL FRAMEWORK | **RATIONAL EXPECTATIONS**

Does ABCT survive a rational expectations critique?

  • Assume a continuum of investors
  • Investors have a normal distribution such that: $i ∼ N(i_N, σ_i)$
  • ABCT dynamics are driven by the marginal investor, not by the average (representative) investor
  • Those who think $i_{LOW}$ is the equilibrium value are **willing** and **able** to displace those who think $i_N$ is the correct value

### ABCT

FINANCIAL FRAMEWORK | RATIONAL EXPECTATIONS | **EMPIRICS**

Strategy

  • Use the EVA framework
    • Use EVA (perceived profits) and $W$ (net investment) as dependent variables
    • Then:
      • $\frac{\partial \text{EVA}}{\partial i} < 0$
      • $\frac{\partial W}{\partial i} < 0$
    • Variables of interest
      • Short-term interest rate (monetary policy)
      • Long-term interest rate (relevant for investors)

### ABCT

FINANCIAL FRAMEWORK | RATIONAL EXPECTATIONS | **EMPIRICS**

Strategy (cont...)

  • Use the EVA framework (cont…)
    • Then, build an econometric model
      • Statistical test on different size of $\beta$ for $i$
      • ARMA(p,q) model
      • IRF from a VAR(p) model

FINANCIAL MICROFOUNDATIONS

### FINANCIAL MICROFOUNDATIONS

EVA VS FCF

### FINANCIAL MICROFOUNDATIONS

EVA VS FCF

Advantages of EVA over FCF

  • EVA is a cleaner representation
    • Does not mix investment with operational costs
    • Works with percentages and economic terms
    • Has an explicit variable for (financial) capital

### FINANCIAL MICROFOUNDATIONS

EVA VS FCF | **VALUE DRIVERS**

Go more micro... $$ \begin{align} ROIC &= \frac{NOPAT}{w} \\\\[10pt] ROIC &= \frac{\frac{NOPAT}{TR}×TR}{W} \\\\[10pt] ROIC &= \frac{\frac{TR - C_1 - … - C_n}{TR}×TR}{W} \end{align} $$

### FINANCIAL MICROFOUNDATIONS

EVA VS FCF | **VALUE DRIVERS**

Go more micro... $$ \begin{align} ROIC &= \left[ 1 - \frac{C_1}{TR} - … - \frac{C_n}{TR} \right] \frac{TR}{W} \\\\[10pt] ROIC &= \left[ \left(\frac{Ω_1}{TR} … \frac{Ω_m}{TR} \right) - \left(\frac{C_1}{TR} - … - \frac{C_n}{TR} \right) \right] \\\\[10pt] ROIC &= \left[ \left( ω_1 + … + ω_m \right) - \left(φ_1 + … + φ_n \right) \right] \end{align} $$

### FINANCIAL MICROFOUNDATIONS

EVA VS FCF | **VALUE DRIVERS**

Go more micro...

  • You can use the value drivers to capture Cantillon effects
  • The value driver gives an estimation of the size of its effect
  • Which relative prices are more and which ones are less impactful

### FINANCIAL MICROFOUNDATIONS

EVA VS FCF | VALUE DRIVERS | **EVA VS ECONOMIC PROFITS**

EVA is the financial equivalent of EP

  • Assume $w$ is the price of all inputs (labor and others)
  • Assume $L$ is the quantity of all inputs (labor and others)

### FINANCIAL MICROFOUNDATIONS

EVA VS FCF | VALUE DRIVERS | **EVA VS ECONOMIC PROFITS**

EVA is the financial equivalent of EP $$ \begin{align} π &= pq - wL - iW \\\\[10pt] π &= \left( \frac{pq - wL}{W} - i \right) W \end{align} $$

Then

  • $CV = W_0 + ∑_{t=1}^{\infty} \left(\frac{p_t q_t - w_t L_t }{W_{t-1}} - i_t \right) W_{t-1}$

FUTURE AREAS OF RESEARCH

### FUTURE AREAS OF RESEARCH

ALERTNESS

Look at $MVA$

  • $CV = W_0 + MVA$
  • Can $MVA$ be the financial equivalent of Kirzner’s alertness?

### FUTURE AREAS OF RESEARCH

ALERTNESS | **MANAGERIAL ECONOMICS**

Look at investment

  • Whether an expense is considered a cost or an investment is subjective
  • The value of EVA depends on whether an expense is a cost or an investment
  • Therefore, the value $CV$ depends on whether an expense is a cost or an investment
  • Two dimensions of subjective value:
    • External: The cash-flow that builds MVA
    • Internal: Whether an expense is considered a cost or an investment by the investor

### FUTURE AREAS OF RESEARCH

ALERTNESS | MANAGERIAL ECONOMICS | **DEVELOPMENT**

Use EFW as a framework

  • Map how changes in each EFW sub-index affects $CV$
  • You have tractable and well-defined marginal effects of policy and institutional shocks
  • EFW sub-indices
    • Area 1: Size of government
    • Area 2: Legal system and property rights
    • Area 3: Sound money
    • Area 4: Freedom to trade internationally
    • Area 5: Regulation