Outline

• Key References

• Definition: What are durables?

• Why measure durables?

• How to measure durables?

  • Flow of services

  • User cost of durables

• Data requirements

• Caveats

• Conclusion

Key References

Deaton, A., and S. Zaidi. 2002. "Guidelines for constructing consumption aggregates for welfare analysis." LSMS Working Paper No. 135,

Amendola, N., and G. Vecchi. 2014. "Durable goods and poverty measurement." World Bank Policy Research Working Paper 7105.

Key References

Deaton, A., and S. Zaidi. 2002. "Guidelines for constructing consumption aggregates for welfare analysis." LSMS Working Paper No. 135,

Amendola, N., and G. Vecchi. 2014. "Durable goods and poverty measurement." World Bank Policy Research Working Paper 7105.

Definitions

• A durable good is a consumption good that can deliver useful services to a consumer through repeated use over an extended period of time (Diewert, 2009)

• A consumer durable is a good that may be used for purposes of consumption repeatedly or continuously over a period of a year or more (SNA, 200).

So,...

• Durable goods are consumer products that
  • withstand wear and tear or decay
  • can be used over a relatively long period without being depleted or consumed

Why measure durables?

• Long-lived goods (automobiles, appliances, furniture) have a positive and significant impact on living standards.

  • Time-saving (e.g. household appliances, transport means)

  • Entertainment (TV, DVD, etc) and communications (Phones)

• Poor households sometimes devote some expenditures to non-food items, including durable goods (Haughton and Khandker, 2009)

• Their inclusion ensures utility consistency.

• Failure to include durable goods may underestimate inequality (to be discussed later).

Do you think of any other reason?

Essence of the problem

There is an inconsistency between the reference period and the period of time in which durable goods deliver their utility to the consumer.

Let's see

According to Deaton (1997, 151), "we need to decide the reference period for welfare measurement, whether someone is poor if they go without adequate consumption or income for a week, a month, or a year"

• The same reference period must be applied to all the components of the welfare aggregate.
• Even if durables are not purchased during the period of reference, households derived utility from those durable goods that were bought in previous periods.

How to measure durables

• Market price of a durable good is not adequate because the it corresponds to the value of its entire economic life, while what we need is the value of the use during the period of reference.

• Principle: we need to estimate the consumption flow of durable goods, which is the benefit accruing to the household from the ownership of durable goods, limited to the reference period.

In short,

• The durables’ service flow exceeds the reference period of the welfare aggregate

• The purchasing price reflects the value of the durable for its entire life

• Need to capture the value of the flow of the service during the reference period

Theoretical framework

Consumption flow $CF$

The consumption flow could be represented as follows,

$$CF_t = k_{v,t}^s \times p_{v,t}^s$$

where,

• $p_{v,t}^s$ is the market price of the good in time $t$;

• $k_{v,t}^s$ is a fraction of the market price,

  • which is accounted as the consumption flow of the good.

• $(t-v)$ refers the year in which the good was manufactured;

• $(t-s)$ the year in which the good was purchased.

Three approaches to estimate $CF$

• Acquisition approach

• Rental equivalence

• User cost

Acquisition approach

If the good is purchased during the reference period, its entire value is attributed to the household welfare aggregate.

$$k_{v,t}^s(a) = \begin{cases} 1 \text{ if } s = 0 \\ 0 \text{ if } s > 0 \end{cases}$$

• $CF = 0$ if household does not purchase the durable good during time $t$ (i.e., $s > 0$),

• $CF_t = P_{v,t}^0$, otherwise.

• $P_{v,t}^0$ captures the current value of all services provided by the durable good. So,...

• This approach assigns the household the entire stream of current and future productive services of the durable in year $t$.

Rental equivalence

If a complete set of markets for the services of durables exists, we can use the market rental value of the goods.

$$k_{v,t}^s(r) = \frac{R_{v,t}}{P_{v,t}^s}$$ where,

• $R_{v,t}$ is the market rental value of the $v$-year old durable good.

• $\frac{R_{v,t}}{P_{v,t}^s}$ rental ratio with respect to the market value of the durable owned by the household, also known as capitalization rate.

• $CF_t = R_{v,t}$

User cost

The annual cost of holding the stock of each durable good is based on a conceptual experiment in which the household buys the durable good at the beginning of each year $t$, and then sell it at the end of the year $t+1$.

$$UC_t = (1+r_t)p_{v,t}^s - p_{v+1,t}^{s+1}$$

Where, $r_t$ is the real interest rate in period $t$.

Durable goods in World Bank's selected poverty assessment reports

A quick Exercise

Calculate the (annual) user cost of a watch that you purchased at $25 a year ago, and it is worth $20 right now. Assume that real interest rate is 10%.

User cost of durables

The previous equation could be rewritten as follow for the total number of durables,

$$UC=\sum_{d=1}^D(S_{td}\times p_{td}(i_t - \pi_t + \delta_d))$$

$S_t$: Quantity of the durable

$p_t$: Price of the durable at the time of purchase

$i_t$: Nominal interest rate

$\pi_t$: Inflation rate

$\delta$: Depreciation rate

$D$: Total number of durables considered

Components of the user cost

• Nominal interest rate $(i_t)$: There are many options. The most common are:

  • Interest rate on safe assets like yields of government bonds (If one assumes that risk aversion and wealth are negatively correlate (Arrow 1971) ).

  • Interest rates on loans of durable goods like cars or other major durables.

• Quantity of the durable $(S_t)$: Comes from the survey. Sometimes it is not available.

• Price of the durable at the time of purchase $(p_t)$: Comes from the survey.

• Inflation rate $(\pi_t)$: Generally, the CPI is used.

• Depreciation rate $(\delta)$: Tricky part that will be discussed bellow

Depreciation rate

In general, the relationship between the price in $t$ of the good $v$-year old, $(p_{v,t})$, and its market value as new, $(p_{0,t})$, may be described as,

$$p_{v,t} = \prod_{i=1}^v(1- \delta_i)p_{0,t}$$

• This relationship depends on the sequence $\{\delta_i\}_{i=1}^v$, which has many ways of calculate it.

  • Geometric depreciation model

  • Straight line depreciation

  • "light bulb" depreciation

  • Mixture depreciation model

Depreciation rate

In general, the relationship between the price in $t$ of the good $v$-year old, $(p_{v,t})$, and its market value as new, $(p_{0,t})$, may be described as,

$$p_{v,t} = \prod_{i=1}^v(1- \delta_i)p_{0,t}$$

• This relationship depends on the sequence $\{\delta_i\}_{i=1}^v$, which has many ways of calculate it.

  • Geometric depreciation model

  • Straight line depreciation

  • "light bulb" depreciation

  • Mixture depreciation model

Empirical implementation of the geometric depreciation model

We assume that the depreciation rate is constant over time, so $\delta_i = \delta$ for every $i$.

case 1

From the survey:

• Current Value for each item = $p_{v,t}$
• Age of each item in years = $v$
• Initial Value for each item = $p_{0,t}$

From other sources:

• Nominal interest rate = $r_t$
• Inflation rate = $\pi_t$

Solution Case 1

Estimation of depreciation rate:

$$\delta - \pi = 1 - (\frac{p_{v,t}}{p_{o,t}})^\frac{1}{v}$$

• In order to minimize the influence of any outliers in the data, it is better to use the median value of depreciation rates of all the goods collected in the survey.

• Thus, household-specific values are not recommended.

case 2

From the survey:

• Current Value for each item = $p_t^d$

• Age of each item in years = $T$

• value of the item when new is not available

From other sources:

• Nominal interest rate = $r_t$

• Inflation rate = $\pi_t$

Solution Case 2

• Calculate the average age of each durable good $\bar{v}$

• Estimate the average lifetime of each durable good as $2\bar{v}$

  • Assumption: purchases are uniformly distributed throughout time

• The, the remaining life of each good is $2\bar{v} - v$

• a rough estimate would be $$\delta - \pi = 1 - (\frac{p_{v,t}}{2\bar{v} - v})^\frac{1}{v}$$

Estimation problems

• Due to high data requirement, measurement errors can be considerable.

  • How do we precisely estimate a depreciation rate for all durables?

• The user cost approach take no account of often considerable transaction costs (e.g., buying and selling durable goods)

Conclusion

1. Durable goods

   • withstand wear and tear or decay

   • used over a relatively long period

2. We measure durables because

   • Poor households purchase durable goods

   • Ensure utility consistency

3. We are interested in the use of a durable good that contributes to welfare

4. Data requirements are high – simplifying assumptions may be necessary.

5. Takes no account of often considerable transaction costs