Section 3 Input Output Analysis

3.1 Overview

Job creation is often estimated through a technique known as input-output analysis. Initially developed by Wassily Leontief in the 1930s, the model has grown in popularity to become the most common method by which nation states, large investment projects, and academics estimate indirect impacts in an economy.

Input-Output analysis is can be used to calculate a number of measures of interest such as revenue, income, and jobs. When used to quantify the full impact of an increase in economic activity resulting from an intervention, this is called impact analysis. The three main components of impact that are generally evaluated are:

A. Direct Effects: The net change in revenue (or jobs, income, etc.) for the beneficiary generated by the intervention.

B. Indirect Effects: the increase in revenue (or jobs, income, etc.) due to additional spending in the supply chain of the direct revenue. By design, these effects are economy-wide, so to estimate the indirect effects attributable to MSEs, the total indirect impact needs to be discounted by a set of coefficients that estimate the proportion of the total sector that are MSEs.

C. Induced Effects: The increased revenue (or jobs, income, etc.) generated from the continued spending of additional wages that have resulted from the intervention

The combination of A + B are typically termed Type I effects, and the combination of A + B + C are termed Type II effects. For present purposes, the rest of this paper will principally be concerned with Type I effects.

3.2 Mathematical Overview

A brief overview of the model is given below. For a thorough treatment of the subject, consult Miller and Blair’s introductory text, Input-Output Analysis: Foundations and Extensions.3

3.2.1 Indirect Impacts on Revenue

Input-output analysis amounts to solving a system of linear equations. Using matrix notation, the general form for the analysis follows the formula

\[ \begin{aligned} \textbf{x} = (\textbf{I} - \textbf{A})^{-1}\textbf{f} \end{aligned} \]

Where, for sectors 1 through \(n\), \(\Delta\textbf{x}\) is an \(n\)-dimensional vector representing the net change in economic output, \(\Delta\textbf{f}\) is a \(n\)-dimensional vector representing the net change in the final demand, \(\textbf{I}\) is a \(n \times n\) identity matrix, and \(\textbf{A}\) is an matrix representing a set of technical coefficients. The term \((\textbf{I} - \textbf{A})^{-1}\) is commonly named the Leontief Inverse.

The technical coefficients \(\textbf{A}\) can be interpreted as follows: for a given sector in column \(j\), the row \(i\) for a given sector represents the monetary value of (domestic) input needed from sector to produce a single unit of output for that sector \(j\). The matrix is calculated as

\[ \begin{aligned} \textbf{A} = \textbf{Z} \widehat{\textbf{x}}^{-1} \end{aligned} \]

Here, \(\widehat{\textbf{x}}\) denotes a square matrix with the elements of \(\textbf{x}\) placed on the diagonal. In contrast to \(\Delta\textbf{x}\), which represents a given change in output, \(\textbf{x}\) represents the total output for the Jordanian economy (i.e. total GDP, broken out into \(n\) sectors). \(\textbf{Z}\) is a matrix that captures the inter-industry intermediary transactions; that is, the amount of money spent by sector \(j\) in purchasing items from sector \(i\) during the course of a year. Stated differently, a given column \(j\) in \(\textbf{Z}\) represents \(i\)’s inputs. Both \(\textbf{Z}\) and \(\textbf{x}\) are made available for \(n = 23\) sectors in the Siyaha Report.

For impact analysis, where the interest lies in estimating the net difference in impact rather than the total value of an economy, the equation is modified slightly to

\[ \begin{aligned} \Delta\textbf{x} = (\textbf{I} - \textbf{A})^{-1}\Delta\textbf{f} \end{aligned} \]

Depending on the analysis of interest, the \(\textbf{A}\) matrix may capture either domestic or total (domestic + international) flows between sectors. For the purposes of LENS and the Siyaha report,4 the domestic impact is of much greater interest, since the project would like to estimate the indirect impact created for Jordanians, not businesses abroad. As a result, the monetary value of foreign imports is purposely excluded from these coefficients, exclusively capturing domestically produced inputs.

In order to calculate indirect revenue, the final step is to subtract the difference in direct impact from the difference in total impact

\[ \begin{aligned} \text{change in direct revenue} = \Delta\textbf{x} - \Delta\textbf{f} \end{aligned} \]

3.2.2 Impacts on Jobs

The Input-Output equations allow analysts to estimate the indirect revenue generated from direct revenue. Other indirect impacts, such as changes to income or jobs, are generally calculated as a function \(f(\cdot)\) of this indirect revenue:

\[ \begin{aligned} \text{indirect jobs} &= f(\text{change in indirect revenue}) \\ &= f(\Delta\textbf{x} - \Delta\textbf{f}) \end{aligned} \]

In the context of jobs, this approach is known as a simple multiplier, as it estimates the impact on employment in relation to the change in indirect revenue. As with the direct impact, it relies heavily on the assumption of constant linear returns. Using this approach, a sector-specific ratio is calculated as the total employment in a sector \(j\) divided by the sector’s total economic output. These sector coefficients can be represented by a vector, \(\textbf{w}\).

\[ \begin{aligned} w_j = \frac{\text{total employment in sector } j}{\text{total output of sector } j} \end{aligned} \]

3.2.3 Is it justified?

The simple multiplier approach relies on the assumption that number jobs and the economy move together.

To see other countries, see the World Bank’s development indicator on GDP per person employed.

Looking at the past 20 years or so, labor productivity has typically increased by 500 dollars (PPP constant 2011 dollars) every year for a given country. The model accounts for 95.6% of the variability in productivity.

Some stats and research about labor productivity.5

Talk about Okun’s law, which holds that the unemployment rate rises and falls with the growth rate of its economy.6

A number of studies have been written on the predicitive capacity of this relationship.7

3.3 Known Limitations

It should be noted that the above jobs/output ratios may underestimate the employment impact on MSE employment. This would be the case if the ratio of the jobs created per dinar of revenue differs substantial between MSEs and large businesses. A rough estimate taken from USAID LENS data of beneficiaries reveals that 1/3 of the labor of LENS grantees is informal (typically family members). If this holds across the wider economy, figures could be adjusted by 4/3 to account for the informal job creation.

3.4 Critical Assessment of the Model

Questions the analyst should as herself:

  • Does your workforce data capture your target population?
  • What is the impact of the shadow economy on the analysis?
  • To what extent can a desired impact be related to an increase in input?
  • How significant is misclassification error?

These questions are not easy to answer, and their answers often harder to swallow. But they must be understood in the context of development: an environment where decisions have to be made with imperfect and lacking information, and where the alternative often boils down to guesswork that can be orders of magnitude greater in error.

3.5 Frequently Asked Questions

1. Isn’t an Input-Output table from 2006 too old?

No. Due to the expense and labor cost needed to produce an IO table, it is the norm rather than the exception that IO tables typically get published 5-10 years after the reference year in which data is collected. This trend is even more common in developing countries. For example, the Siyaha report (published in 2013) and WFP analysis (published in 2014) both utilize reference data from 2006. Although it is always more desirable to use more recent data, a 10-year old table should not be considered to be outdated. Likewise, using employment ratios from 2006 may also be more consistent with the 2006 JIOT data, as well as staying relatively stable over time.

2. Isn’t the Siyaha Input-Output table only valid for the tourism sector?

Not really. The Siyaha input-output table must, by nature, be economy-wide in order to estimate the full impact of an investment in tourism on the Jordanian economy. Although the multipliers in the report are select for for the tourism sectors of interest, multipliers can be calculated on the same basis for any of the 23 sectors. The basic components of the report— \(\textbf{x}\), \((\textbf{I} - \textbf{A})^{-1}\), and \(\textbf{f}\)– are all economy-wide. The one aspect in which the Siyaha table may be somewhat ‘tourism specific’ is the way in which the IO table has been reduced from 81 sectors to 23 sectors. This is done mainly for reasons pertaining to mathematical stability as well as precision of estimates. However, implicit in this process is the decision on which sectors to collapse together. To the extent that one of the 23 sectors is overly-general in capturing a specific intervention, there may be aggregation bias. This could be resolved by creating separate LENS-specific sectors if LENS were able to get the \(81 \times 81\) table.

3. How reliable is the IO table?

Input-Output tables can be especially costly to develop, and so a great deal of effort and time is generally devoted to ensuring that such an investment will lead to quality data. Although no guarantee of quality, DoS has received technical support from a number of foreign states in developing these tables, most notably from Statistics Denmark. In evaluating the reliability of IO analysis, it should be noted that that there is just as much—if not more— room for error resulting in improper estimation of direct revenue changes. Whereas the overall multipliers are consistent with international benchmarks, it is quite possible that the revenue figures will be much harder to estimate due to measurement and specification error on the part of LENS. As with any model, the mantra of garbage-in-garbage-out applies: estimated impacts coming out of the model will only be as good as the quality of the inputs fed into it.

4. Who else uses the JIOT?

USAID,8 the UN World Food Program, and a number of academics (see references).

5. Won’t matrix algebra be too complicated for M&E staff to manage?

Although the initial calculation of the Leontief Inverse can be complicated for the uninitiated, once derived, not further linear algebra is necessary. All subsequent analysis can be done with a calculator or in Microsoft Excel. The total indirect impact can be calculated as the weighted sum of each sector’s direct inputs multiplied by that sector’s multiplier, and most other indirect impacts require only sector-specific multiplication of inputs by fixed coefficients.

6. How large of an undertaking will it be for LENS to adopt the IO approach?

Since the principal components of the JIOT exist and are readily available for 23 sectors, the major effort required on the part of LENS is not with respect building the model itself, but mainly in generating values for the net change in revenue resulting from LENS interventions. This said, some effort will be required in creating (1) a set of sector coefficients that attribute the proportion of sector output to MSEs, and (2) a set of employment MSE-specific coefficients that estimate the ratio of jobs per 1000 JOD of revenue.

  1. Ronald E. Miller and Peter D. Blair, Input-Output Analysis: Foundations and Extensions, 2nd ed. (Cambridge University Press, 2009). ↩

  2. “Indirect Impact of Tourism in Jordan” (Building Economic Sustainability Through Tourism Project (USAID Siyaha), May 2013), www.siyaha.org/sites/default/files/Documents/Report.pdf. ↩

  3. Paul Schreyer and Dirk Pilat, “Measuring Productivity,” OECD Economic Studies 33, no. 2 (2001): 5, http://www.oecd.org/social/labour/1959006.pdf. ↩

  4. Martin F. J. Prachowny, “Okun’s Law: Theoretical Foundations and Revised Estimates,” The Review of Economics and Statistics 75, no. 2 (1993): 331–36, http://www.jstor.org/stable/2109440. ↩

  5. See, for instance, Edward S. Knotek II, “How Useful Is Okun’s Law?” Economic Review-Federal Reserve Bank of Kansas City 92, no. 4 (2007): 73, https://www.kansascityfed.org/Publicat/ECONREV/PDF/4q07Knotek.pdf and Laurence Ball, João Tovar Jalles, and Prakash Loungani, “Do Forecasters Believe in Okun’s Law? An Assessment of Unemployment and Output Forecasts,” International Journal of Forecasting 31, no. 1 (2015): 176–84, https://www.imf.org/external/pubs/ft/wp/2014/wp1424.pdf. ↩

  6. “Indirect Impact of Tourism in Jordan.” ↩