6 Equations Stock-Flow Model

The Inventory Dynamics Model describes the equilibrium dynamics and cyclicality of the real estate market. (The model is associated with Kenneth Rosen, William Wheaton, Patric Hendershott, and others.)

The core model consists of six equations, though it can be modified (as I did to adapt it to the Tbilisi market). The content of the equations is as follows:

1. Development Equation: New developments occur in proportion to rent levels. Additionally, if rent (and thus real estate prices) falls below a certain threshold, new construction halts (i.e., higher profitability increases motivation). The model accounts for the long-term nature of the sector and includes a delayed response to rent levels of about three years.
2. Total Stock Equation: The total stock in the market equals the sum of existing and newly developed properties.
3. Demand Equation: Demand depends on both total need (e.g., for office spaces, the number of employees) and rent levels. It is a classic linear equation with elasticity and intercept coefficients.
4. Occupied Space Equation: It is assumed that the occupied space equals last year’s demand, as satisfying demand is a process that cannot happen instantaneously.
5. Vacancy Rate Equation: The vacancy rate equals the total stock minus the occupied space.
6. Rent Price Equation: Rent depends on the amount of vacant space. If the vacancy rate exceeds a normal threshold, rents decrease, and vice versa.

The model’s essence lies in demonstrating the sector’s cyclical nature. According to an example in the referenced book, the results show:

On the horizontal axis are years, while the vertical axes are adjusted to interesting dimensions (rent in $, growth in demand, construction in sq. m., and vacancy rate as a percentage). The yellow curve (new developments) exhibits a strongly cyclical character due to small changes in rent and vacancy rates. The intuition behind the graphs is simple: due to the sector’s long-term nature, it cannot react instantly to supply-demand equilibrium, leading to periodic market replenishment.

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Tbilisi Residential Market:

Modifications to the Model:

• Added depreciation to the total stock equation.
• Transformed rents into prices by adding Cap Rate and Rent-Price equations.
• Adjusted the development equation: In reality, even if rents drop significantly, new construction does not stop entirely. Thus, I assumed that the number of new projects is halved (instead of reduced to zero) if rents fall below a certain threshold.

Assumptions:

Below, I explain why certain figures were included in the assumptions. Some are based on statistics, while others are intuitive and open to debate. For this reason, I conducted a sensitivity analysis on the assumptions.

• Supply Sensitivity (0.4): The slope of the supply curve was taken as symmetric to demand, assuming a delayed reaction of three years. The curve is not vertical.
• Demand Sensitivity (-0.4): Derived from statistical data in the G&T research reports: Tbilisi Residential Real Estate, November 2024.
• Technology (20 sq. m.): A term from the book, referring to the average space occupied per person. This figure underpins initial model inputs, such as total supply (calculated by multiplying population by space per capita) and total demand.
• Demand Intercept (1.5 million sq. m.): A statistically derived number fitted to the model. Conceptually, it represents the maximum possible demand at a very low price level.
• Rent Sensitivity (0.4): Assumed equal to supply sensitivity, reflecting rent price elasticity concerning vacancy rates.
• Rent Threshold ($8/sq. m.): Indicates the rent per square meter below which developers reduce supply. Lower rents mean lower sale prices and diminished motivation for new construction.
• Current (10%) and Long-Term (6%) Cap Rates: Adopted based on local market studies and seemed reasonable during discussions with Copilot.
• Tbilisi Population (1.26 million) and current rent ($10/sq. m.): Based on available sources and local intuition.
• Current and Normal Vacancy Rates (10%): Chosen intuitively, representing the proportion of spaces naturally unoccupied at any given time.
• Population Growth Rate (1%): A semi-statistical and semi-intuitive figure sourced from historical data on Geostat.ge.
• Housing Stock Depreciation (3.2%): Assumes 25% of buildings are depreciated and will become uninhabitable within 20 years, while the rest will depreciate over 80 years on average. Added 1% to account for Tbilisi’s conditions.
• Current Average Price ($1200/sq. m.): A statistical figure.
• New Construction Supply (1.5 million sq. m. annually): Estimated from annual building permits, assuming yearly supply matches permits.

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Results:

Each parameter significantly impacts the critical $780/sq. m. threshold shown in the graph. A sensitivity analysis was conducted to understand how 20% deviations from assumptions influence this value.

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Reality Check:

• Supply Sensitivity: If the average space per capita is higher than 20 sq. m., the total stock and demand will also be larger. Consequently, the annual supply proportion to the existing stock will be lower, presenting a more optimistic picture.
• Demand Expansion: While population size drives demand in the model, increasing incomes per capita could lead to demand for larger living spaces, creating a similarly optimistic outlook.
• Inflation: The model also does not account for inflation, which, if integrated, would increase the long-term slope of the price curve, providing a more positive perspective.

One certainty is that maintaining high economic growth rates and fostering population growth is crucial to avoiding sector stagnation. Reducing annual building permits is neither realistic nor advisable.

Excel Model

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Adapted from: Commercial Real Estate Analysis and Investments by D. M. Geltner, N. G. Miller, J. Clayton, P. Eichholtz

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