Discussing the Importance of Stationary Residuals in Time Series

A traditional approach of analyzing the residuals in regression models can be identified over the Classical Assumptions in Linear Models (Rodríguez Revilla, 2014), which primarily involves the residuals in aspects as homoscedasticity, no serial correlation (or auto-correlation), no endogeneity, correct specification (this one includes no omitted variables, no redundant variables, and correct functional form) and finally, normal distribution among the estimated residuals of the model with expected zero mean.

In time series context, residuals must be stationary in order to avoid spurious regressions (Woolridge, 2012), if there are no properties of
stationarity among the residuals, then basically our results tend to produce
fake relationships in our model. At this point, it is convenient to say:

“A stationary time series
process is one whose probability distributions are stable over time in the
following sense: if we take any collection of random variables in the sequence
and then shift that sequence ahead h times periods, the joint probability
distribution must remain unchanged”
(Woolridge, 2012, pág. 381)

Another definition according to Lutkepohl & Kratzig (2004) says that stationarity has time-invariant first and second moments over a single variable, mathematically:

Equation (1) simply implies that the expected values of the y process must have a constant mean, so the stationary process must fluctuate around a constant mean defined in µ, no trends are available in the process. Equation
(2) is telling us that variances are time-invariant, so the term γ, doesn’t depend on t but just on the distance h.

In order to get a better notion of stationarity, we define that a stationary process follows the pattern in the next graph. Which was generated using random values over a constant mean of 0, and with a normal probability distribution. The time period sample was n=500 observations.

The generated process fluctuates around a constant mean, and no tendency is present. How do we confirm if the series is normally distributed? Well, we can perform a histogram over the series. In Stata, the command is histogram y, norm where y is our variable.

The option of ,norm is given in Stata in order to present the actual normal distribution, so we can see that real distribution it’s not far from it. We can graphically affirm that series might present a normal distribution, but in order to confirm it, we need to do a formal test, so we perform Jarque-Bera test with the command sktest y

The null hypothesis of the test is that normal distribution exists among the y variable And since p-value is bigger than a 5%significance level, we fail to reject null hypothesis and we can say that y variable is normally distributed.

Checking for unit roots also is useful when we’re trying to discover stationarity over a variable, so we perform first, the estimated ideal lag for the test, with varsoc y which will tell us what appropriated lag-length should be used in the ADF test.

Such results, indicate that ADF test over y variable must be done with one lag according to FPE, AIC, while HQIC and SBIC indicate 0 lags. It is the decision of the investigator to select the right information criteria (mostly it is selected when all error criteria are in a specific lag). However, we have a draw of FPE and AIC vs HQIC and SBIC. We will discard FPE since according to Liew (2004) this one is more suitable for samples lower than 120 observations, and thus we will select 0 lag for the test considering our sample size of 500 observations.

Null hypothesis is the existence of unit roots in the variable, so we can strongly reject this and accept that no-unit roots are present. Sometimes this test is used to define stationarity of a respective process, but we need to take in consideration that stationarity involves constant means and normal distributions. We can say for now, that y variable is stationary.

At this point, one could argue Why we need the notion of stationarity over the residuals? This is because stationarity ensures that no spurious regressions are estimated. Now let’s assume we have a model which
follows an I (0) stationary model.

And that I (0) variables are y and x, common intuition will tell us that u will be also stationary, but we need to ensure this. Proceeding with our Monte Carlo approaches, we generated the x series with a constant mean which has a normal distribution and that with u ~ (0,1) as the Data Generating Process of y expressed in equation (3). Basically u has a mean of 0, and variance of 1. Regressing y on x we got the next result.

We can see that coefficients B_0 and B_1 are approximated 1 and 2 respectively, so it’s almost close to the data generating process and both estimators are statistically significant at 1%. Let’s look at the residuals of the estimated model a little bit closer, we start by predicting the residuals using the command predict u, residuals in order to get the predicted values. Then we perform some of the tests we did before.

Graphic of the residuals with tsline u presentsthe next result, which looks like a stationary process.

A histogram over the residuals, will show the pattern
of normal distribution.

And as well, the normality test will confirm this result.

Now we need to test that the residuals don’t follow a unit root pattern, a consideration here must be done first before we use ADF test, and is that critical values of the test are not applicable to the residuals. Thus, we cannot fully rely on this test.

In Stata we can recur to the Engle-Granger distribution test of the residuals, to whether accept or reject the idea that residuals are stationary. So, we type egranger y x which provides an accurate estimate of the critical values to evaluate the residuals.

As tests evidence, Test statistic is pretty close between ADF test and Engle & Granger test but the critical values are way different. Furthermore, we should rely on the results of the Engle & Granger test. Since Test statistic is bigger than 5% critical value, we can reject the null hypothesis that x and y are not cointegrated, and we can affirm that both variables present over this estimation a long run path of equilibrium. From another view, implies that the residuals are stationary and our regression is not spurious.

This basic idea can be extended with I (1) variables, in order to test whether it exists a long run path and if the regression model in (3) turns to be super consistent. Then long-run approximations with error correction forms can be done for this model where all variables are I (1).

This idea of testing residuals in stationary models is not a formal test used in the literature, however, it can reconfirm that with I (0) models that the regression will not be spurious. And it can also help to contrast long-run relationships.

Note: The package egranger must be installed first ssc install egranger, replace should do the trick. This package parts from the regression model to be estimated, however, it has the failure it cannot be computed with time operators. So, generating first differences or lagged values must be done in separate variables.


Liew, V. (2004). “Which Lag Length Selection Criteria Should We Employ?”. Journal of Economics Bulletin, 1-9. Recuperated from:

Lutkepohl, H., & Kratzig, M. (2004). Applied Time Series Econometrics. Cambridge: Cambridge university press.

Rodríguez Revilla, R. (2014). Econometria I y II. Bogotá. : Universidad Los

Woolridge, J. (2012). Introductory Econometrics. A Modern Approach 5th edition. United States: South Western Cengage Learning.

The evil in the heart of the good: Unfolding the role of remittances in the escalating trade deficit figures of the MENA region.


The MENA region is ranked first in terms of remittance receipts (3.83% of GDP) worldwide, it has also the highest non-oil trade deficit among other developing regions (World Bank, 2018). This study uses panel data from 11 Labor-abundant MENA countries (main destination of remittance receipts) to examine the trade balance effect of remittances. We postulate that the main driver of the trade deficit in the MENA region is the weak industrial sector, which fails to provide domestic substitutes for imports of manufactured products (El Wassal 2012). Based on our hypothesis, we imply that in countries with weaker domestic absorptive capacity, the excessive demand of remittance-recipient families will not be compensated by domestic production, but rather imports of the consumption good, thus worsening the trade balance deficit.

The empirical work from the MENA region on the trade balance effects of remittances is limited. Bouhga-Hagbe (2004) supported the evidence of this effect in Morocco, wherein remittances covered the trade deficit and contributed to the observed surpluses of the external current account. Kandil and Mirzaie (2009) showed that remittances promote both exports and imports in Jordan while nourishing only exports in Tunisia. In the case of Egypt, El Sakka, and McNabb (1999) reported that imports financed through remittances have a high-income elasticity, thereby implying
that they are either consumer durables or purchased by high-income groups. In a study, involving interviews of 304 remittance-receiving families across 16 Egyptian governorates during 2015–2016, Farzanegan et al. (2017) examined further the causes and effects of
remittances. Using a panel of 17 remittances receiving countries in the MENA and Central Asia regions over a period of 1990–2009, Abdih et al. (2012) concluded that a significant portion of remittances is
used to purchase foreign goods.

Our empirical results confirm the import triggering effects of remittances, however these effects are mitigated as the investment capacity of a country gets stronger and become able to neutralize foreign purchases with domestic products. Many policymakers are pushing to increase remittances as a reliable source of income by reducing transfer costs. The real challenge is promoting the productive use of these remittances in financing domestic production capabilities and non-oil exports. The channel of promoting domestic capital formation through encouraging private savings and productive use of remittances could improve the balance of trade. This can be realized by promoting financial services, which targets repatriates and their families, like saving incentives, interest rate premium on migrant’s deposits, and the issuance of remittances back bonds. Although
remittances may carry some development-related outcomes, such as income smoothing, reducing poverty, and promoting education, the applied literature is still equivocal about the magnitude of these effects and the governing conditions to realising these effects. Our paper is an
example of a study that has highlighted a rather countercyclical effect of the
inflow of remittances on the recipient countries’ trade balance. This piece of
evidence among others suggests that promoting remittances does not always come in favour for the recipient economies and is conditioned to the prevailing economic and institutional environments.


Mohammad Reza Farzanegan & Sherif Maher Hassan (2019) How does the flow of remittances affect the trade balance of the Middle East and North Africa?, Journal of Economic Policy Reform, DOI: 10.1080/17487870.2019.1609357

Oil war: GCC stability Vs. EU stability


After the dramatic turmoils that took place in France and then have spread across other European countries. These turmoils were mainly triggered by the hikes in Oil prices in the last few months, These surges have caused rigorous supply shock to prices, causing thousands maybe million of Mid-class people in EU to struggle. Lives casts from Paris and Belgium brought back memories from the Arab spring in early 2011, the similar domino effect of the tragedic sequences where people get into the streets to demand something, then other people who suffer from a different thing – etc. labor reforms- use the chance and start raising their voices, a different group, farmers start asking for higher prices for their products, an escalations of social frustration that build on as days pass by.

However these problems start to loosen up as oil prices start to sharply decline again, and as this was the main trigger for these social escalations, it was the main lessor for these as well. besides other measures that were adopted by these countries’ governments, but none of these could have worked without first the stabilization and reduction of oil prices. OPEC countries that are dominated by GCC oil hubs such as Saudi Arabia, UAE, and Kuwait have been pushed to increase oil production and this will automatically bring down oil prices. A strategy that indeed comes in favor of these conflicted first class developed countries, yet it does not necessarily come in the favor of the people living in oil exporting countries, especially in such times where domestic inflation rates in Saudi Arabia and UAE are escalating, budget deficits in the new Saudi Budget reaches historical records, however, the political pressure simply cannot be overseen. GCC countries have to react in favor for the big ones instead of their people, as oil is their major budget components, few dollars reduction in its prices will cause millions of budget revenue to be lost.

One lesson here is that the economy is no longer free, the political influence of the big ones govern economic laws of supply and demand as well as the strategic products prices. However, for developing countries, governments need to fight back against this political dominance and strongly hold to the power of rejection to decide what’s good for their own people.

General guidelines of scientific writing

An excerpt from Manikw’s blog 

When I was CEA chair, I sent the following guidelines to my staff as they started drafting the Economic Report of the President. A friend recently emailed me a copy, and I thought I would share them with blog readers. They are good rules of thumb, especially for economists writing for a general audience.

ERP Writing Guidelines

· Stay focused. Remember the take-away points you want the reader to remember. If some material is irrelevant to these points, it should probably be cut.

· Keep sentences short. Short words are better than long words. Monosyllabic words are best.

· The passive voice is avoided by good writers.

· Positive statements are more persuasive than normative statements.

· Use adverbs sparingly.

· Avoid jargon. Any word you don’t read regularly in a newspaper is suspect.

· Never make up your own acronyms.

· Avoid “of course, “clearly,” and “obviously.” Clearly, if something is obvious, that fact will, of course, be obvious to the reader.

· The word “very” is very often very unnecessary.

· Keep your writing self-contained. Frequent references to other works, or to things that have come before or will come later, can be distracting.

· To mere mortals, a graphic metaphor, a compelling anecdote, or a striking fact is worth a thousand articles in Econometrica.

· Keep your writing personal. Remind readers how economics affects their lives.

· Remember two basic rules of economic usage: o “Long run” (without a hyphen) is a noun. “Long-run” (with a hyphen) is an adjective. Same with “short(-)run.” o “Saving” (without a terminal s) is a flow. “Savings” (with a terminal s) is a stock.

· Buy a copy of Strunk and White’s Elements of Style. Also, William Zinsser’s On Writing Well. Read them—again and again and again.

· Keep it simple. Think of your reader as being your college roommate who majored in English literature. Assume he has never taken an economics course, or if he did, he used the wrong textbook.

Why minimum wages and why not?


Understanding the economic intuition behind minimum wages
law is of great importance, given the economic fluxes spreading all over the
world, from the Arab spring in Middle East, to budget deficits in USA and the debt crises in euro zone. Regarding the debatable and controversial outcomes of minimum wages, I will try to explain why governments tend to be quite hesitant when it comes to agree on such law settlement.

A typical labor market with an upward supply of labor that shows the number of employees willing to work at different wages levels, it
might be viewed as the marginal cost (MC) of each additional unit of
labor. The demand curve for labor by employers at given fixed level of Marginal productivity and price level is downward slopping; any changes in those exogenous variables would lead to inward/outward shifts in this curve. The equilibrium wage and No. of workers are determined at the intersection of the two curves at W*, L*.

The government may at any point of time intervene and set a price floor for wages (wages cannot decrease below this level) in form of a minimum wage that is higher than the equilibrium wage. Why any government think
to apply such law, simply because the government considers the equilibrium wage insufficient for sustaining poor people, so the government uses its legislative authority and force employers to offer workers higher wages than competitive wage level.

Notably to mention that low skilled job seekers are the target group by this law, because low skilled or teenagers who lack the sufficient educational and job experiences have no chance to compete in such market, in
other words, they are more eligible for internships with no payment, or on job training with wages lower than equilibrium wages.

With wages at the minimum floor, we might observe the following:

1- The No. of people who actively seek jobs would rise, this increase in supply of labor might come from existing labor force who were employed as interns or on job trainees, and people who are counted as voluntary unemployed, such wage rate now meet their expectations and force them to get back to the play yard.

2- The cost of hiring workers now is higher, employers are obliged to pay higher wages, which would force them to reduce the demand for employees, except for really skilled, highly efficient ones.

3- The outcome would be a surplus in the labor market, where the supply of labor by employees exceeds the demand for labor by employers.

4- Only highly skilled labor (LD) are being employed and receive the benefits of higher wages “ Not the target group “

5- Teenage unemployment tends to increase, No. of students who drop out of schools might increase (as now it is more tempting to seek jobs than before) , the rate of job creating in the shadow “underground” economy might hike, because of the legal market surplus (No minimum wage laws in shadow economies)

This is not the end of the story, otherwise things would be quite easy and simple, and we can conclude that minimum wages are bad, and
governments should seek better –less costly-ways to do its job for supporting low-income people (i.e. Earned income tax credit).

More than 200 academic researchers have been studying the
effects of minimum wages on labor markets over the last century, and have been trying to observe the patterns of teenage unemployment after setting this wage floor. Opponents argue that it causes unemployment, lead to discrimination for the favor of highly skilled workers (or black people as observed in the minimum wage law settlement in USA during the 1930s), schools drop out increase, illegal and criminal activities increase, inflation rises.

Proponents -on the contrary- argue that minimum wages are
not bad, however, when, how and where they are applied is the crucial issue.
They advocate that minimum wages would hike productivity of workers and
increase the opportunity cost of leisure, moreover the hike in prices would
increase the demand for labor because the accession in employer’s profits, and thus the observed unemployment rise is transitory. In addition, the marginal propensity to consume (MPC) of low income people is much higher than high income people, consequently the whole aggregate demand might rise and instigate the rate of job creation in the economy, not mentioning, moral, ethical norms of providing better life for low income people and the reduction of criminal/illegal acts in the economy.

However, empirical evidence stands for the side of proponents; a typical econometric analysis of this phenomenon has shown that, an increase of 10% in minimum wage would reduce employment by only 1-3%,
depending upon the elasticity of the demand for labor in this market, and the degree of wage raise.

To fully understand the whole picture we should also incorporate our analysis with the case of removal of fringe benefits. Observing
employer’s reaction to the imposed minimum wages, possibly by removing fringe benefits from their employees “transportation, health insurance, memberships, relaxed work conditions, free coupons, etc…” , we might conclude a different outcome, as both employees and employers tend to be worse off in terms of gained utility in favor of lower reduction in employment levels in the labor market.

To recap, each market should be considered separately; there is no general catalog for the spillovers of minimum wages. Governments should
treat such decision very carefully, also to consider the amount of wage raise, the elasticity of the demand in each market, and others law or legalization that might hinder/strut the negative spillovers of minimum wages. Favorably a government could seek better – in sense of controversy- , stable -in sake of predicted outcomes-, and less costly -in terms welfare losses- than this dangerous remedy for poverty.

The interaction between monetary and macroprudential policies

There is an increasing concern among policy makers and economists about macro prudential policies that aim to stabilize the economy and alleviate financial distortions through affecting output and inflation levels . This paper by Claessens, and Valencia, (2013) at VOX tries to study the possible interactions between monetary and macro prudential policies. In addition, it highlights the stylized fact that neither monetary nor fiscal policies are sufficient to stabilize the economy, additional tool is needed to continue this job.

“The newly emerging paradigm is one in which both monetary policy and macro prudential policies are used for counter cyclical management: monetary policy primarily aimed at price stability; and macro prudential policies primarily aimed at financial stability. But these policies interact with each other and thus each may enhance or diminish the effectiveness of the other”

When prices rigidities are the only distortion, then momentary policy goal of stabilizing prices will also stabilize output and maximize welfare, but in the presence of financial market imperfections, which affect people expectations and predicted risks, this will hinder the influence of monetary policy on output stabilization. If this is the case, then monetary policy is not enough, because financial distortions might not directly/indirectly be related to liquidity levels. A combination of both monetary and macroprudential policies -with one focusing on liquidity and other focusing on altering aggregate demand of this liquidity- to reduce financial risks and stabilize the economy is required.

Urban slums and their implications for national fertility rate


With the expected increase in world population by one billion people in just over a decade, governments in less developed countries are faced with the challenge of having to accommodate the majority of this future population growth. This is of concern since many of these countries currently face various social, economic and infrastructural challenges that impede their ability to adequately accommodate this increase in people. One such challenge is how to deal with the current issue of their large and youthful populations, many of which are located in slums in large cities. A large youthful population presents many opportunities for stimulating economic growth, and for building a more civil and educated community. However, as can be seen in the context of developing countries, especially those in Sub-Saharan Africa, wrestling with this problem continues
to be an ongoing challenge.

A related issue to population growth is that of high fertility rates in less developed countries. While many such countries have made remarkable strides in order to reduce fertility rates, for some countries, progress has been slow. For other countries, for example, those within the MENA and SSA developing regions, substantial progress has been made towards
reducing fertility rates; however fertility rates in these regions still
continue to be among the highest in the world. Developing regions have much larger slum populations compared to developed regions. This is in part owing to the failure of governments in these regions to adequately meet the demands (e.g., housing and jobs) of their growing population. As a result, existing slums expand and new slums emerge in order to informally accommodate the needs of this growing population. Given the typically high fertility rates in slum communities and the larger presence of slums in
less developed countries that are currently facing the most pressing population growth and fertility issues, this study hypothesized that slums are in part responsible for fertility rates variations amongst less developed countries.

Analyzing data from a sample of 72 countries in the developing world, our results support the prior hypothesis that slums affect countries’
fertility rates. More specifically, the results of this study showed that an
increase in the number of slum dwellers leads to a subsequent small increase in fertility rates. Additional drivers for fertility rates identified were contraceptive prevalence, female education, and infant mortality, all of which are consistent with the literature on fertility dynamics. For example, better-educated women are expected to be more knowledgeable on the use of contraceptive methods and ways of accessing them. These women may also favor fewer kids that can be well taken care of, compared to having large families where resources shared amongst family members may become stretched too thin. As a result, our analyses showed that an increase in female education reduces the instance of fertility rate. Further, while the results for contraceptive prevalence and female
education were consistent across all models derived in this study, the same was not true for infant mortality, with further research needed to examine why this had occurred.

In order to test the robustness of the slum measure, this study used two
measures of slum: (1) the urban slum population as a percentage of the total urban population, and (2) the urban slum population as a percentage of total population. The results of such analysis showed a similar small increase in fertility rate with the increase in the number of slum dwellers. Such empirical findings are important since they suggest that while the magnitude of slums’ impact in affecting countries’ fertility rates may be small, with the increased  growth of these communities, this impact may become magnified in the future due to the multiplier effect. Thus, in order to adequately address the fertility rate issues that less developing countries are experiencing, governments in these countries should take a more active role in better managing their slum populations.

Reference: Hassan, S.M., and Mahabir, R.S. (2018). Urban slums and fertility rate differentials. Population Review, 57(2):47-74.

What looks like a discount is not actually a discount

What is the goal of any firm,  store, mall, service provider or even a rocket factory? The answer is, either earning enough money(Accounting profit) to run the business, and cover operational costs (variable costs), or filling the stakeholder pocket’s with more profits (Economic profits), which include the accounting profit in its calculation and the opportunity cost forgone from running a different business.

Let us keep it simple, firms aim to make economic profits, but it would not
mind so much if it is stuck with accounting profits.What can firms do? Well
this requires good managers, financial analysts, smart accountants, production factors, and some microeconomics

Assume that we have a firm that is doing a good job, or it has some power over its prices, hence, this market is an imperfect competitive market. The Demand curve of this firm’s product/service is downward, which means higher prices would distort sales. Nevertheless, remember that higher prices mean more bucks in the pockets. Therefore, firms always have an incentive to charge higher prices, along with selling more products to accesses their economic profits, while equating the firm’s marginal revenue with marginal cost (Profit maximizing condition)

Firms can use magicians to flip aside the demand curve and make it upward slopping. Unfortunately, I cannot recommend the former trick, because I suspect its applicability. However, Microeconomics proposes a different trick.

Firms can achieve this by more costly and sophisticated ways, either establishing good connections with Government officials to restrict entering this market along with producing a product that is needed and has no close substitutes (AKA. monopolist), or to dowhat is known as imperfect price discrimination (Market segmentation).

The idea here is to sell the same product at different prices for different consumers, depending upon their price sensitivities. Conclusively, people who tend to be more sensitive (segment 2) should be assigned lower prices; others should have high prices (Segment 1). As elasticity rises, people will be willing to pay lower prices for this product or service, because of their preferences, accessibility of closer substitutes, income, age, etc…. For example, when you regularly do your weekly shopping from the grocery store nearby, and a big, shiny advertisement blocks your way, which
announces that you can buy more of your favorite jam with lower price, buy one with 40 cents, 2 with 75 cents and three with 1.05 cent. Your mind
automatically deduce the total price of buying 3 single jars with 40 cents each (price of a single jar in this offer) and the total price of 3 jars in this
offer(1.05 cents), so the difference will save you 15 cents.

This is what I was talking about, this offer is not for the sake of consumers, otherwise the grocery manager is trying to price discriminate you ( or run you along your demand curve) and guess what he always wins. Because the profit from selling only one jam jar with say 30 cents (lowest price possible to instigate sales) is lower than his profit from the discrimination strategy (both cases, he assign a price higher than his marginal cost). Therefore, what looks like a discount for you, is simply a technique of profits accession for the owner.

Successful Price discrimination based upon the uniqueness of sold product and the inability to resell this product (Taking benefit from price differentials between consumers). We can find price discrimination strategies in airline industries at which the price of last minute traveler ticket is higher than regular ticket prices (regular in sense of their rush and the opportunity cost of their times which determines their willingness to pay).

At cinemas, children are usually offered lower ticket prices, because they tend to buy pop corn, cola and stuff, which would cover up the discounted value of their tickets. Juniors tend to have discounts at their outlets, because they are price sensitive, and tend to have more time to search for cheaper alternatives than older people do.

Tip for sellers:

– Your challenge is to find ways to know people willingness to pay while segmenting your markets (as people do not walk with their elasticity coefficients on their shirts), make unique products, and make it harder to resell your sold units. The more accurate you deduce the degree of sensitivity of your costumers, the more successfully you will be able to price discriminate and earn more profits.

Tip for buyers

– Do not be so inelastic; do not give any signals implicitly or explicitly to sellers that you are eager to buy this product now, and spend some time searching for better and cheaper alternatives.

Sure thing, this simple analysis misses a lot of salient information about firm’s pricing and producing behaviors.